Journal articles on the topic 'Quillen equivalence'

This paper proves that the q-model structures of Moore flows and of multipointed d-spaces are Quillen equivalent. The main step is the proof that the counit and unit maps of the Quillen adjunction are isomorphisms on the q-cofibrant objects (all objects are q-fibrant). As an application, we provide a new proof of the fact that the categorization functor from multipointed d-spaces to flows has a total left derived functor which induces a category equivalence between the homotopy categories. The new proof sheds light on the internal structure of the categorization functor which is neither a left adjoint nor a right adjoint. It is even possible to write an inverse up to homotopy of this functor using Moore flows.

This paper sets up the foundations for derived algebraic geometry, Goerss–Hopkins obstruction theory, and the construction of commutative ring spectra in the abstract setting of operadic algebras in symmetric spectra in an (essentially) arbitrary model category. We show that one can do derived algebraic geometry a la Toën–Vezzosi in an abstract category of spectra. We also answer in the affirmative a question of Goerss and Hopkins by showing that the obstruction theory for operadic algebras in spectra can be done in the generality of spectra in an (essentially) arbitrary model category. We construct strictly commutative simplicial ring spectra representing a given cohomology theory and illustrate this with a strictly commutative motivic ring spectrum representing higher order products on Deligne cohomology. These results are obtained by first establishing Smith’s stable positive model structure for abstract spectra and then showing that this category of spectra possesses excellent model-theoretic properties: we show that all colored symmetric operads in symmetric spectra valued in a symmetric monoidal model category are admissible, i.e., algebras over such operads carry a model structure. This generalizes the known model structures on commutative ring spectra and $\text{E}_{\infty }$-ring spectra in simplicial sets or motivic spaces. We also show that any weak equivalence of operads in spectra gives rise to a Quillen equivalence of their categories of algebras. For example, this extends the familiar strictification of $\text{E}_{\infty }$-rings to commutative rings in a broad class of spectra, including motivic spectra. We finally show that operadic algebras in Quillen equivalent categories of spectra are again Quillen equivalent. This paper is also available at arXiv:1410.5699v2.

AbstractThe purpose of this paper is to study pro excision in algebraicK-theory and cyclic homology, after Suslin–Wodzicki, Cuntz–Quillen, Cortiñas, and Geisser–Hesselholt, as well as continuity properties of André–Quillen and Hochschild homology. A key tool is first to establish the equivalence of various pro Tor vanishing conditions which appear in the literature.This allows us to prove that all ideals of commutative, Noetherian rings are pro unital in a suitable sense. We show moreover that such pro unital ideals satisfy pro excision in derived Hochschild and cyclic homology. It follows hence, and from the Suslin–Wodzicki criterion, that ideals of commutative, Noetherian rings satisfy pro excision in derived Hochschild and cyclic homology, and in algebraicK-theory.In addition, our techniques yield a strong form of the pro Hochschild–Kostant–Rosenberg theorem; an extension to general base rings of the Cuntz–Quillen excision theorem in periodic cyclic homology; a generalisation of the Feĭgin–Tsygan theorem; a short proof of pro excision in topological Hochschild and cyclic homology; and new Artin–Rees and continuity statements in André–Quillen and Hochschild homology.

Abstract By careful analysis of the embedding of a simplicial set into its image under Kan’s $$\mathop {\mathop {\mathsf {Ex}}^\infty }$$Ex∞ functor we obtain a new and combinatorial proof that it is a weak homotopy equivalence. Moreover, we obtain a presentation of it as a strong anodyne extension. From this description we can quickly deduce some basic facts about $$\mathop {\mathop {\mathsf {Ex}}^\infty }$$Ex∞ and hence provide a new construction of the Kan–Quillen model structure on simplicial sets, one which avoids the use of topological spaces or minimal fibrations.

AbstractThe category of rational SO(2)–equivariant spectra admits an algebraic model. That is, there is an abelian category ${\mathcal A}$(SO(2)) whose derived category is equivalent to the homotopy category of rational SO(2)–equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra?The category ${\mathcal A}$(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non–Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on ${\mathcal A}$(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K(p)–local stable homotopy category.A monoidal Quillen equivalence to a simpler monoidal model category R•-mod that has explicit generating sets is also given. Having monoidal model structures on ${\mathcal A}$(SO(2)) and R•-mod removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)–equivariant spectra.

The purpose of this paper is to introduce the notion of a CW complex over a topological category. The main theorem of this paper gives an equivalence between the homotopy theory of diagrams of spaces based on a topological category and the homotopy theory of CW complexes over the same base category.A brief description of the paper goes as follows: in Section 1 we introduce the homotopy category of diagrams of spaces based on a fixed topological category. In Section 2 homotopy groups for diagrams are defined. These are used to define the concept of weak equivalence and J-n equivalence that generalize the classical definition. In Section 3 we adapt the classical theory of CW complexes to develop a cellular theory for diagrams. In Section 4 we use sheaf theory to define a reasonable cohomology theory of diagrams and compare it to previously defined theories. In Section 5 we define a closed model category structure for the homotopy theory of diagrams. We show this Quillen type homotopy theory is equivalent to the homotopy theory of J-CW complexes. In Section 6 we apply our constructions and results to prove a useful result in equivariant homotopy theory originally proved by Elmendorf by a different method.

We present a way of constructing a Quillen model structure on a full subcategory of an elementary topos, starting with an interval object with connections and a certain dominance. The advantage of this method is that it does not require the underlying topos to be cocomplete. The resulting model category structure gives rise to a model of homotopy type theory with identity types, Σ- and Π-types, and functional extensionality. We apply the method to the effective topos with the interval object ∇2. In the resulting model structure we identify uniform inhabited objects as contractible objects, and show that discrete objects are fibrant. Moreover, we show that the unit of the discrete reflection is a homotopy equivalence and the homotopy category of fibrant assemblies is equivalent to the category of modest sets. We compare our work with the path object category construction on the effective topos by Jaap van Oosten.

AbstractThe homotopy coherent nerve from simplicial categories to simplicial sets and its left adjoint are important to the study of (∞, 1)-categories because they provide a means for comparing two models of their respective homotopy theories, giving a Quillen equivalence between the model structures for quasi-categories and simplicial categories. The functor also gives a cofibrant replacement for ordinary categories, regarded as trivial simplicial categories. However, the hom-spaces of the simplicial category X arising from a quasi-category X are not well understood. We show that when X is a quasi-category, all Λ21 horns in the hom-spaces of its simplicial category can be filled. We prove, unexpectedly, that for any simplicial set X, the hom-spaces of X are 3-coskeletal. We characterize the quasi-categories whose simplicial categories are locally quasi, finding explicit examples of 3-dimensional horns that cannot be filled in all other cases. Finally, we show that when X is the nerve of an ordinary category, X is isomorphic to the simplicial category obtained from the standard free simplicial resolution, showing that the two known cofibrant “simplicial thickenings” of ordinary categories coincide, and furthermore its hom-spaces are 2-coskeletal.

AbstractA Quillen model structure on the category Gray-Cat of Gray-categories is described, for which the weak equivalences are the triequivalences. It is shown to restrict to the full subcategory Gray-Gpd of Gray-groupoids. This is used to provide a functorial and model-theoretic proof of the unpublished theorem of Joyal and Tierney that Gray-groupoids model homotopy 3-types. The model structure on Gray-Cat is conjectured to be Quillen equivalent to a model structure on the category Tricat of tricategories and strict homomorphisms of tricategories.

A reparametrization category is a small topologically enriched symmetric semimonoidal category such that the semimonoidal structure induces a structure of a commutative semigroup on objects, such that all spaces of maps are contractible and such that each map can be decomposed (not necessarily in a unique way) as a tensor product of two maps. A Moore flow is a small semicategory enriched over the closed semimonoidal category of enriched presheaves over a reparametrization category. We construct the q-model category of Moore flows. It is proved that it is Quillen equivalent to the q-model category of flows. This result is the first step to establish a zig-zag of Quillen equivalences between the q-model structure of multipointed d-spaces and the q-model structure of flows.

We introduce the concept of infinite cochain sequences and initiate a theory of homological algebra for them. We show how these sequences simplify and improve the construction of infinite coclass families (as introduced by Eick and Leedham-Green) and also how they can be applied to prove that almost all groups in such a family have equivalent Quillen categories. We also include some examples of infinite families of$p$-groups from different coclass families that have equivalent Quillen categories.

AbstractWe introduce a notion of n-quasi-categories as fibrant objects of a model category structure on presheaves on Joyal's n-cell category Θn. Our definition comes from an idea of Cisinski and Joyal. However, we show that this idea has to be slightly modified to get a reasonable notion. We construct two Quillen equivalences between the model category of n-quasi-categories and the model category of Rezk Θn-spaces, showing that n-quasi-categories are a model for (∞, n)-categories. For n = 1, we recover the two Quillen equivalences defined by Joyal and Tierney between quasi-categories and complete Segal spaces.

AbstractWe prove that the category of trees Ω is a test category in the sense of Grothendieck. This implies that the category of dendroidal sets is endowed with the structure of a model category Quillen-equivalent to spaces. We show that this model category structure, up to a change of cofibrations, can be obtained as an explicit left Bousfield localisation of the operadic model category structure.

In this paper we give for any r, n, 0 [les ] r [les ] n, a Quillen's model structure to the category of simplicial groups where the weak equivalences are those morphisms f[bull ] such that πq(f[bull ]) is an isomorphism for r [les ] q [les ] n. This is carried out by studying the cases r = 0 and n → ∞ previously and, in each one of them, we make explicit some constructions for the associated homotopy theories, such as the cylinder and path objects and the loop and suspension functors, and we also relate the simplicial homotopy relation to the homotopy relation obtained from these structures.

AbstractThe Lusternik–Schnirelmann category has been described in different ways. Two major ones, the first by Ganea, the second by Whitehead, are presented here with a number of variants. The equivalence of these variants relies on the axioms of Quillen's model category, but also sometimes on an additional axiom, the so-called “cube axiom”.

AbstractWe study Quillen's model category structure for homotopy of simplicial objects in the context of Janelidze, Márki and Tholen's semi-abelian categories. This model structure exists as soon as is regular Mal'tsev and has enough regular projectives; then the fibrations are the Kan fibrations of S. When, moreover, is semi-abelian, weak equivalences and homology isomorphisms coincide.

We introduce what is meant by an AC-Gorenstein ring. It is a generalized notion of Gorenstein ring that is compatible with the Gorenstein AC-injective and Gorenstein AC-projective modules of Bravo–Gillespie–Hovey. It is also compatible with the notion of $n$ -coherent rings introduced by Bravo–Perez. So a $0$ -coherent AC-Gorenstein ring is precisely a usual Gorenstein ring in the sense of Iwanaga, while a $1$ -coherent AC-Gorenstein ring is precisely a Ding–Chen ring. We show that any AC-Gorenstein ring admits a stable module category that is compactly generated and is the homotopy category of two Quillen equivalent abelian model category structures. One is projective with cofibrant objects that are Gorenstein AC-projective modules while the other is an injective model structure with fibrant objects that are Gorenstein AC-injectives.

In this paper, I give a generalized analogue of the string topology results of Chas and Sullivan, and of Cohen and Jones. For a finite simplicial complex $X$ and $k \geq 1$, I construct a spectrum $Maps(S^k, X)^{S(X)}$, which is obtained by taking a generalization of the Spivak bundle on $X$ (which however is not a stable sphere bundle unless $X$ is a Poincaré space), pulling back to $Maps(S^k, X)$ and quotienting out the section at infinity. I show that the corresponding chain complex is naturally homotopy equivalent to an algebra over the $(k + 1)$-dimensional unframed little disk operad $\mathcal{C}_{k + 1}$. I also prove a conjecture of Kontsevich, which states that the Quillen cohomology of a based $\mathcal{C}_k$-algebra (in the category of chain complexes) is equivalent to a shift of its Hochschild cohomology, as well as prove that the operad $C_{\ast}\mathcal{C}_k$ is Koszul-dual to itself up to a shift in the derived category. This gives one a natural notion of (derived) Koszul dual $C_{\ast}\mathcal{C}_k$-algebras. I show that the cochain complex of $X$ and the chain complex of $\Omega^k X$ are Koszul dual to each other as $C_{\ast}\mathcal{C}_k$-algebras, and that the chain complex of $Maps(S^k, X)^{S(X)}$ is naturally equivalent to their (equivalent) Hochschild cohomology in the category of $C_{\ast}\mathcal{C}_k$-algebras.

AbstractIn a paper from 2002, Hovey introduced the Gorenstein projective and Gorenstein injective model structures on R-Mod, the category of R-modules, where R is any Gorenstein ring. These two model structures are Quillen equivalent and in fact there is a third equivalent structure we introduce: the Gorenstein flat model structure. The homotopy category with respect to each of these is called the stable module category of R. If such a ring R has finite global dimension, the graded ring R[x]/(x2) is Gorenstein and the three associated Gorenstein model structures on R[x]/(x2)-Mod, the category of graded R[x]/(x2)-modules, are nothing more than the usual projective, injective and flat model structures on Ch(R), the category of chain complexes of R-modules. Although these correspondences only recover these model structures on Ch(R) when R has finite global dimension, we can set R = ℤ and use general techniques from model category theory to lift the projective model structure from Ch(ℤ) to Ch(R) for an arbitrary ring R. This shows that homological algebra is a special case of Gorenstein homological algebra. Moreover, this method of constructing and lifting model structures carries through when ℤ[x]/(x2) is replaced by many other graded Gorenstein rings (or Hopf algebras, which lead to monoidal model structures). This gives us a natural way to generalize both chain complexes over a ring R and the derived category of R and we give some examples of such generalizations.

The proposal of the Quilmes Tectonic Trough (Fosa tectónica de Quilmes – FQ) as the extension of the southern end of the Santa Lucía basin in Uruguay and its connection to the Salado basin in Argentina suggest the existence of a large sedimentary volume capable of housing a new aquifer on the La Plata River coast. However, the sedimentary volumes that form the FQ are hidden under a thick, recently deposited cover, and thus, there is a lack of studies on the nature of this formation. Nevertheless, the Uruguayan section of the Meso-Cenozoic depocenter of the Santa Lucía basin has been more thoroughly studied for hydrocarbon exploration, which enabled us to estimate the equivalent tectosedimentary characteristics in the FQ. In the Uruguayan territory, three aquifer systems of the Santa Lucía basin are exploited: the Raigón (Plio-Pleistocene) aquifer, which is the most important source of groundwater for various uses in the south-central region of Uruguay, and the Mercedes (Upper Cretaceous) and Migues (Lower Cretaceous) aquifers, which are also used, albeit to a lesser extent, for drinking water, irrigation, and industrial purposes. The Migues aquifer, the least known of the three, shows a variable depth ranging from 100 to 1500 m and considerable stratigraphic sequences of porous and permeable sandstones. These sandstones provide the aquifer with very good qualities as a reservoir rock; as such, the Migues aquifer has been studied for its potential natural gas reserves and geothermal and water resources. Accordingly, if the same sequences with equivalent sedimentary and hydrogeological qualities are present in the FQ, similar aquifers with interesting properties may remain unidentified along the Buenos Aires coast beneath the intensely explored Puelches, Pampeano and Paraná aquifers. In conclusion, specific exploratory activities may prove the existence and quality of these hydrogeological resources, the regional slope toward the southwest from the Uruguayan outcrops, upwelling or semiupwelling conditions and even geothermal energy associated with the deepest cretaceous aquifers.

We investigate the assumptions under which a subclass of flat quasicoherent sheaves on a quasicompact and semiseparated scheme allows us to ‘mock’ the homotopy category of projective modules. Our methods are based on module-theoretic properties of the subclass of flat modules involved as well as their behaviour with respect to Zariski localizations. As a consequence we get that, for such schemes, the derived category of flat quasicoherent sheaves is equivalent to the derived category of very flat quasicoherent sheaves. If, in addition, the scheme satisfies the resolution property then both derived categories are equivalent to the derived category of infinite-dimensional vector bundles. The equivalences are inferred from a Quillen equivalence between the corresponding models.

AbstractWe prove that four different ways of defining Cartesian fibrations and the Cartesian model structure are all Quillen equivalent: On marked simplicial sets (due to Lurie [31]), On bisimplicial spaces (due to deBrito [12]), On bisimplicial sets, On marked simplicial spaces. The main way to prove these equivalences is by using the Quillen equivalences between quasi-categories and complete Segal spaces as defined by Joyal–Tierney and the straightening construction due to Lurie.

Abstract For any given subgroup H of a finite group G, the Quillen poset ${\mathcal {A}}_p(G)$ of nontrivial elementary abelian p-subgroups is obtained from ${\mathcal {A}}_p(H)$ by attaching elements via their centralisers in H. We exploit this idea to study Quillen’s conjecture, which asserts that if ${\mathcal {A}}_p(G)$ is contractible then G has a nontrivial normal p-subgroup. We prove that the original conjecture is equivalent to the ${{\mathbb {Z}}}$ -acyclic version of the conjecture (obtained by replacing ‘contractible’ by ‘ ${{\mathbb {Z}}}$ -acyclic’). We also work with the ${\mathbb {Q}}$ -acyclic (strong) version of the conjecture, reducing its study to extensions of direct products of simple groups of p-rank at least $2$ . This allows us to extend results of Aschbacher and Smith and to establish the strong conjecture for groups of p-rank at most $4$ .

Abstract We construct a calculus of functors in the spirit of orthogonal calculus, which is designed to study ‘functors with reality’ such as the Real classifying space functor, $\BU_\Bbb{R}(-)$ . The calculus produces a Taylor tower, the n-th layer of which is classified by a spectrum with an action of $C_2 \ltimes \U(n)$ . We further give model categorical considerations, producing a zigzag of Quillen equivalences between spectra with an action of $C_2 \ltimes \U(n)$ and a model structure on the category of input functors which captures the homotopy theory of the n-th layer of the Taylor tower.

We obtain geometric models for the infinite loop spaces of the motivic spectra $\mathrm{MGL}$, $\mathrm{MSL}$, and $\mathbf{1}$ over a field. They are motivically equivalent to $\mathbb{Z}\times \mathrm{Hilb}_\infty^\mathrm{lci}(\mathbb{A}^\infty)^+$, $\mathbb{Z}\times \mathrm{Hilb}_\infty^\mathrm{or}(\mathbb{A}^\infty)^+$, and $\mathbb{Z}\times \mathrm{Hilb}_\infty^\mathrm{fr}(\mathbb{A}^\infty)^+$, respectively, where $\mathrm{Hilb}_d^\mathrm{lci}(\mathbb{A}^n)$ (resp. $\mathrm{Hilb}_d^\mathrm{or}(\mathbb{A}^n)$, $\mathrm{Hilb}_d^\mathrm{fr}(\mathbb{A}^n)$) is the Hilbert scheme of lci points (resp. oriented points, framed points) of degree $d$ in $\mathbb{A}^n$, and $+$ is Quillen's plus construction. Moreover, we show that the plus construction is redundant in positive characteristic. Comment: 13 pages. v5: published version; v4: final version, to appear in \'Epijournal G\'eom. Alg\'ebrique; v3: minor corrections; v2: added details in the moving lemma over finite fields

Obscured in contemporary climate change discourse is the fact that under even the most serious mitigation scenarios being envisaged it will be virtually impossible to avoid runaway ecosystem collapse; so great is the momentum of global greenhouse build-up (Anderson and Bows). And under even the best-case scenario, two-degree warming, the ecological, social, and economic costs are proving to be much deeper than first thought. The greenhouse genie is out of the bottle, but the best that appears to be on offer is a gradual transition to the pro-growth, pro-consumption discourse of “ecological modernisation” (EM); anything more seems politically unpalatable (Barry, Ecological Modernisation; Adger et al.). Here, I aim to account for how cheaply EM has managed to allay ecology. To do so, I detail the operations of the co-optive, definitional strategy which I call the “high-ground” strategy, waged by a historic bloc of actors, discourses, and institutions with a common interest in resisting radical social and ecological critique. This is not an argument about climate laggards like the United States and Australia where sceptic views remain near the centre of public debate. It is a critique of climate leaders such as the United Kingdom, Germany, and the Netherlands—nations at the forefront of the adoption of EM policies and discourses. With its antecedent in sustainable development discourse, by emphasising technological innovation, eco-efficiency, and markets, EM purports to transcend the familiar dichotomy between the economy and the environment (Hajer; Barry, ‘Towards’). It rebuts the 1970s “limits to growth” perspective and affirms that “the only possible way out of the ecological crisis is by going further into the process of modernisation” (Mol qtd. in York and Rosa 272, emphasis in original). Its narrative is one in which the “dirty and ugly industrial caterpillar transforms into an ecological butterfly” (Huber, qtd. in Spaargaren and Mol). How is it that a discourse notoriously quiet on endless growth, consumer culture, and the offshoring of dirty production could become the cutting edge of environmental policy? To answer this question we need to examine the discursive and ideological effects of EM discourse. In particular, we must analyse the strategies that work to continually naturalise dominant institutions and create the appearance that they are fit to respond to climate change. Co-opting Environmental Discourse Two features characterise state environmental discourse in EM nations: an almost universal recognition of the problem, and the reassurance that present institutions are capable of addressing it. The key organs of neoliberal capitalism—markets and states—have “gone green”. In boardrooms, in advertising and public relations, in governments, and in international fora, climate change is near the top of the agenda. While EM is the latest form of this discourse, early hints can be seen in President Nixon’s embrace of the environment and Margaret Thatcher’s late-1980s green rhetoric. More recently, David Cameron led a successful Conservative Party “detoxification” program with an ostentatious rhetorical strategy featuring the electoral slogan, “Vote blue, go green” (Carter). We can explain this transformation with reference to a key shift in the discursive history of environmental politics. The birth of the modern environmental movement in the 1960s and 70s brought a new symbolic field, a new discourse, into the public sphere. Yet by the 1990s the movement was no longer the sole proprietor of its discourse (Eder 203). It had lost control of its symbols. Politicians, corporations, and media outlets had assumed a dominant role in efforts to define “what climate change was and what it meant for the world” (Carvalho and Burgess 1464). I contend that the dramatic rise to prominence of environmental issues in party-political discourse is not purely due to short-term tactical vote-winning strategy. Nor is it the case that governments are finally, reluctantly waking up to the scientific reality of ecological degradation. Instead, they are engaged in a proactive attempt to redefine the contours of green critique so as to take the discourse onto territory in which established interests already control the high ground. The result is the defusing of the oppositional element of political ecology (Dryzek et al. 665–6), as well as social critique in general: what I term the gentrification of climate change. If we view environmentalism as, at least partially, a cultural politics in which contested definitions of problem is the key political battleground, we can trace how dominant interests have redefined the contours of climate change discourse. We can reveal the extent to which environmentalism, rather than being integrated into capitalism, has been co-opted. The key feature of this strategy is to present climate change as a mere aberration against a background of business-as-usual. The solutions that are presented are overwhelmingly extensions of existing institutions: bringing CO2 into the market, the optimistic development of new techno-scientific solutions to climate problems, extending regulatory regimes into hitherto overlooked domains. The agent of this co-optive strategy is not the state, industry, capital, or any other manifest actor, but a “historic bloc” cutting across divisions between society, politics, and economy (Laclau and Mouffe 42). The agent is an abstract coalition that is definable only to the extent that its strategic interests momentarily intersect at one point or another. The state acts as a locus, but the bloc is itself not reducible to the state. We might also think of the agent as an assemblage of conditions of social reproduction, in which dominant social, political, and economic interests have a stake. The bloc has learned the lesson that to be a player in a definitional battle one must recognise what is being fought over. Thus, exhortations to address climate change and build a green economy represent the first stage of the definitional battle for climate change: an attempt to enter the contest. In practical terms, this has manifest as the marking out of a self-serving division between action and inaction. Articulated through a binary modality climate change becomes something we either address/act on/tackle—or not. Under such a grammar even the most meagre efforts can be presented as “tackling climate change.” Thus Kevin Rudd was elected in 2007 on a platform of “action on climate change”, and he frequently implored that Australia would “do its bit” on climate change during his term. Tony Blair is able to declare that “tackling climate change… need not limit greater economic opportunity” and mean it in all sincerity (Barry, ‘Towards’ 112). So deployed, this binary logic minimises climate change to a level at which existing institutions are validated as capable of addressing the “problem,” and the government legitimised for its moral, green stand. The Hegemonic Articulation of Climate Change The historic bloc’s main task in the high-ground strategy is to re-articulate the threat in terms of its own hegemonic discourse: market economics. The widely publicised and highly influential Stern Review, commissioned by the British Government, is the standard-bearer of how to think about climate change from an economic perspective. It follows a supremely EM logic: economy and ecology have been reconciled. The Review presents climate change, famously, as “the greatest market failure the world has ever seen” (Stern et al. viii). The structuring horizon of the Stern Review is the correction of this failure, the overcoming of what is perceived to be not a systemic problem requiring a reappraisal of social institutions, but an issue of carbon pricing, technology policy, and measures aimed at “reducing barriers to behavioural change”. Stern insists that “we can be ‘green’ and grow. Indeed, if we are not ‘green’, we will eventually undermine growth, however measured” (iv). He reassures us that “tackling climate change is the pro-growth strategy for the longer term, and it can be done in a way that does not cap the aspirations for growth of rich or poor countries” (viii). Yet Stern’s seemingly miraculous reconciliation of growth with climate change mitigation in fact implies a severe degree of warming. The Stern Review aims to stabilise carbon dioxide equivalent concentrations at 550ppm, which would correspond to an increase of global temperature of 3-4 degrees Celsius. As Foster et al. note, this scenario, from an orthodox economist who is perceived as being pro-environment, is ecologically unsustainable and is viewed as catastrophic by many scientists (Foster, Clark, and York 1087–88). The reason Stern gives for not attempting deeper cuts is that they “are unlikely to be economically viable” (Stern et al. 231). In other words, the economy-ecology articulation is not a meeting of equals. Central to the policy prescriptions of EM is the marketising of environmental “bads” like carbon emissions. Carbon trading schemes, held in high esteem by moderate environmentalists and market economists alike, are the favoured instruments for such a task. Yet, in practice, these schemes can do more harm than good. When Prime Minister Kevin Rudd tried to legislate the Carbon Pollution Reduction Scheme as a way of addressing the “greatest moral challenge of our generation” it represented Australia’s “initial foray into ecological modernisation” (Curran 211). Denounced for its weak targets and massive polluter provisions, the Scheme was opposed by environmental groups, the CSIRO, and even the government’s own climate change advisor (Taylor; Wilkinson). While the Scheme’s defenders claimed it was as a step in the right direction, these opponents believed it would hurt more than help the environment. A key strategy in enshrining a particular hegemonic articulation is the repetition and reinforcement of key articulations in a way which is not overtly ideological. As Spash notes of the Stern Review, while it does connect to climate change such issues as distributive justice, value and ethical conflicts, intergenerational issues, this amounts to nothing but lip service given the analysis comes pre-formed in an orthodox economics mould. The complex of interconnected issues raised by climate change is reduced to the impact of carbon control on consumption growth (see also Swyngedouw and While, Jonas, and Gibbs). It is as if the system of relations we call global capitalism—relations between state and industry, science and technology, society and nature, labour and capital, North and South—are irrelevant to climate change, which is nothing but an unfortunate over-concentration of certain gases. In redrawing the discursive boundaries in this way it appears that climate change is a temporary blip on the path to a greener prosperity—as if markets and capitalism merely required minor tinkering to put them on the green-growth path. Markets are constituted as legitimate tools for managing climate change, in concert with regulation internalised within neoliberal state competition (While, Jonas, and Gibbs 81). The ecology-economy articulation both marketises “green,” and “greens” markets. Consonant with the capitalism-environment articulation is the prominence of the sovereign individual. Both the state and the media work to reproduce subjects largely as consumers (of products and politics) rather than citizens, framing environmental responsibility as the responsibility to consume “wisely” (Carvalho). Of course, what is obscured in this “self-greening” discourse is the culpability of consumption itself, and of a capitalist economy based on endless consumption growth, exploitation of resources, and the pursuit of new markets. Greening Technology EM also “greens” technology. Central to its pro-growth ethos is the tapering off of ecosystem impacts through green technologies like solar, wind, tidal, and geothermal. While green technologies are preferable to dependence upon resource-intensive technologies of oil and coal, that they may actually deliver on such promises has been shown to be contingent upon efficiency outstripping economic growth, a prospect that is dubious at best, especially considering the EM settlement is one in which any change to consumption practices is off the agenda. As Barry and Paterson put it, “all current experience suggests that, in most areas, efficiency gains per unit of consumption are usually outstripped by overall increases in consumption” (770). The characteristic ideological manoeuvre of foregrounding non-representative examples is evident here: green technologies comprise a tiny fraction of all large-scale deployed technologies, yet command the bulk of attention and work to cast technology generally in a green light. It is also false to assume that green technologies do not put their own demands on material resources. Deploying renewables on the scale that is required to address climate change demands enormous quantities of concrete, steel, glass and rare earth minerals, and vast programs of land-clearing to house solar and wind plants (Charlton 40). Further, claims that economic growth can become detached from ecological disturbance are premised on a limited basket of ecological indicators. Corporate marketing strategies are driving this green-technology articulation. While a single advertisement represents an appeal to consume an individual commodity, taken collectively advertising institutes a culture of consumption. Individually, “greenwash” is the effort to spin one company’s environmental programs out of proportion while minimising the systemic degradation that production entails. But as a burgeoning social institution, greenwash constitutes an ideological apparatus constructing industry as fundamentally working in the interests of ecology. In turn, each corporate image of pristine blue skies, flourishing ecosystems, wind farms, and solar panels constitutes a harmonious fantasy of green industry. As David Mackay, chief scientific advisor to the UK Government has pointed out, the political rhetoric of green technology lulls people into a false sense of security (qtd. in Charlton 38). Again, a binary logic works to portray greener technologies—such as gas, “clean coal”, and biomass combustion—as green. Rescuing Legitimacy There are essentially two critical forces that are defused in the high-ground strategy’s definitional project. The first is the scientific discourse which maintains that the measures proposed by leading governments are well below what is required to reign in dangerous climate change. This seems to be invisible not so much because it is radical but because it is obscured by the uncertainties in which climate science is couched, and by EM’s noble-sounding rhetoric. The second is the radical critique which argues that climate change is a classic symptom of an internal contradiction of a capitalist economy seeking endless growth in a finite world. The historic bloc’s successful redefinition strategy appears to jam the frequency of serious, scientifically credible climate discourse, yet at the level of hegemonic struggle its effects range wider. In redefining climate change and other key signifiers of green critique – “environment”, “ecology”, “green”, “planet”—it expropriates key properties of its antagonist. Were it not that climate change is now defined on the cheery, reassuring ground of EM discourse, the gravity of the alarming—rather than alarmist (Risbey)—scientific discourse may just have offered radical critique the ammunition it needed to provoke society into serious deliberations over its socioeconomic path. Radical green critique is not in itself the chief enemy of the historic bloc. But it is a privileged element within antagonistic discourse and reinforces the critical element of the feminist, civil rights, and student movements of the 1960s and 1970s. In this way ecology has tended to act as a nodal point binding general social critique: all of the other demands began to be inscribed with the green critique, just as the green critique became a metaphor for all of the others (Laclau). The metaphorical value of the green critique not only relates to the size and vibrancy of the movement—the immediate visibility of ecological destruction stood as a powerful symbol of the kernel of antagonistic politics: a sense that society had fundamentally gone awry. While green critique demands that progress should be conditional upon ecology, EM professes that progress is already green (Eder 217n). Thus the great win achieved by the high-ground strategy is not over radical green critique per se but over the shifting coalition that threatens its legitimacy. As Stavrakakis observes, what is novel about green discourse is nothing essential to the signifiers it deploys, but the way that a common signifier comes to stand in and structure the field as a whole – to serve as a nodal point. It has a number of signifiers: environmental sustainability, social justice, grassroots democracy, and peace and non-violence, all of which are “quilted” around the master-signifiers of “ecology”, “green”, or “planet”. While these master-signifiers are not unique to green ideology, what is unique is that they stand at the centre. But the crucial point to note about the green signifier at the heart of political ecology is that its value is accorded, in large part, through its negation of the dominant ideology. That is to say, it is not that green ideology stands as merely another way of mapping the social; rather, the master-signifier "green" contains an implicit refutation of the dominant social order. That “green” is now almost wholly evacuated of its radical connotations speaks to the effectiveness of the redefinitional effort.The historic bloc is aided in its efforts by the complexity of climate change. Such opacity is characteristic of contemporary risks, whose threats are mostly “a type of virtual reality, real virtuality” (Beck 213). The political struggle then takes place at the level of meaning, and power is played out in a contest to fix the definitions of key risks such as climate change. When relations of (risk) definition replace relations of production as the site of the effects of power, a double mystification ensues and shifts in the ground on which the struggle takes place may go unnoticed. Conclusion By articulating ecology with markets and technology, EM transforms the threat of climate change into an opportunity, a new motor of neoliberal legitimacy. The historic bloc has co-opted environmentalist discourse to promote a gentrified climate change which present institutions are capable of managing: “We are at the fork in the road between order and catastrophe. Stick with us. 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