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Books on the topic 'Topological categories'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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1

Turaev, Vladimir, and Alexis Virelizier. Monoidal Categories and Topological Field Theory. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49834-8.

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2

Lowen, R. Approach spaces: The missing link in the topology-uniformity-metric triad. Oxford: Clarendon Press, 1997.

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3

Tanaka, Hiro Lee. Lectures on Factorization Homology, ∞-Categories, and Topological Field Theories. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61163-7.

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4

Theory of topological structures: An approach to categorical topology. Dordrecht: D. Reidel Pub. Co., 1988.

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5

Functorial knot theory: Categories of tangles, coherence, categorical deformations, and topological invariants. Singapore: World Scientific, 2001.

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6

Werner, Gähler, Preuss Gerhard 1940-, and Herrlich Horst, eds. Categorical structures and their applications: Proceedings of the North-West European Category Seminar, Berlin, Germany, 28-29 March 2003. Singapore: World Scientific, 2004.

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7

A non-Hausdorff completion: The Abelian category of C-complete left modules over a topological ring. New Jersey: World Scientific, 2015.

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8

On the algebraic foundation of bounded cohomology. Providence, R.I: American Mathematical Society, 2011.

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9

Pantev, Tony. Stacks and catetories in geometry, topology, and algebra: CATS4 Conference Higher Categorical Structures and Their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, July 2-7, 2012, CIRM, Luminy, France. Providence, Rhode Island: American Mathematical Society, 2015.

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10

Tulane University. Dept. of Mathematics, ed. Mathematical foundations of information flow: Clifford lectures on information flow in physics, geometry and logic and computation, March 12-15, 2008, Tulane University, New Orleans, Louisiana. Providence, R.I: American Mathematical Society, 2012.

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11

1973-, Johnson Mark W., ed. A foundation for PROPs, algebras, and modules. Providence, Rhode Island: American Mathematical Society, 2015.

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12

Basterra, Maria, Kristine Bauer, Kathryn Hess, and Brenda Johnson. Women in topology: Collaborations in homotopy theory : WIT, Women in Topology Workshop, August 18-23, 2013, Banff International Research Station, Banff, Alberta, Canada. Providence, Rhode Island: American Mathematical Society, 2015.

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13

Ausoni, Christian, 1968- editor of compilation, Hess, Kathryn, 1967- editor of compilation, Johnson Brenda 1963-, Lück, Wolfgang, 1957- editor of compilation, and Scherer, Jérôme, 1969- editor of compilation, eds. An Alpine expedition through algebraic topology: Fourth Arolla Conference, algebraic topology, August 20-25, 2012, Arolla, Switzerland. Providence, Rhode Island: American Mathematical Society, 2014.

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14

Stanford Symposium on Algebraic Topology: Applications and New Directions (2012 : Stanford, Calif.), ed. Algebraic topology: Applications and new directions : Stanford Symposium on Algebraic Topology: Applications and New Directions, July 23--27, 2012, Stanford University, Stanford, CA. Providence, Rhode Island: American Mathematical Society, 2014.

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15

Argentina) Luis Santaló Winter School-CIMPA Research School Topics in Noncommutative Geometry (3rd 2010 Buenos Aires. Topics in noncommutative geometry: Third Luis Santaló Winter School-CIMPA Research School Topics in Noncommutative Geometry, Universidad de Buenos Aires, Buenos Aires, Argentina, July 26-August 6, 2010. Edited by Cortiñas, Guillermo, editor of compilation. Providence, RI: American Mathematical Society, 2012.

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16

Turaev, Vladimir, and Alexis Virelizier. Monoidal Categories and Topological Field Theory. Birkhäuser, 2017.

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17

Turaev, Vladimir, and Alexis Virelizier. Monoidal Categories and Topological Field Theory. Birkhäuser, 2018.

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18

Dimitric, Radoslav. Slenderness: Volume 1, Abelian Categories. Cambridge University Press, 2018.

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19

Hrushovski, Ehud, and François Loeser. An equivalence of categories. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0013.

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This chapter deduces from Theorem 11.1.1 an equivalence of categories between a certain homotopy category of definable subsets of quasi-projective varieties over a given valued field and a suitable homotopy category of definable spaces over the o-minimal Γ‎. The chapter introduces three categories that can be viewed as ind-pro definable and admit natural functors to the category TOP of topological spaces with continuous maps. The discussion is often limited to the subcategory consisting of A-definable objects and morphisms. The morphisms are factored out by (strong) homotopy equivalence. The chapter presents the proof of the equivalence of categories before concluding with remarks on homotopies over imaginary base sets.

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20

Pfeiffer, Christian. Body in Categories 6. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198779728.003.0005.

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This chapter expands on the basic theory, which is presented in the Categories. It offers a treatment of the mereotopological properties of bodies, for instance, what belongs to them insofar as they are bodies of physical substances. Bodies are complete and perfect in virtue of being three‐dimensional. Body is prior to surfaces and lines and, because bodies are complete, there cannot be a four‐dimensional magnitude. The explanation offered is that certain topological properties are linked to and determined by the nature of the object in question. Body is a composite of the boundary and the interior or extension. A formal characterization of boundaries as limit entities is offered and it is argued that boundaries are dependent particulars. Similarly, the extension is ontologically dependent on bodies. Aristotle’s argument that the extension of objects is divisible into ever‐divisibles is revisited.

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21

Kishida, Kohei. Categories and Modalities. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198748991.003.0009.

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Category theory provides various guiding principles for modal logic and its semantic modeling. In particular, Stone duality, or “syntax-semantics duality”, has been a prominent theme in semantics of modal logic since the early days of modern modal logic. This chapter focuses on duality and a few other categorical principles, and brings to light how they underlie a variety of concepts, constructions, and facts in philosophical applications as well as the model theory of modal logic. In the first half of the chapter, I review the syntax-semantics duality and illustrate some of its functions in Kripke semantics and topological semantics for propositional modal logic. In the second half, taking Kripke’s semantics for quantified modal logic and David Lewis’s counterpart theory as examples, I demonstrate how we can dissect and analyze assumptions behind different semantics for first-order modal logic from a structural and unifying perspective of category theory. (As an example, I give an analysis of the import of the converse Barcan formula that goes farther than just “increasing domains”.) It will be made clear that categorical principles play essential roles behind the interaction between logic, semantics, and ontology, and that category theory provides powerful methods that help us both mathematically and philosophically in the investigation of modal logic.

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22

(Translator), I. Tweddle, ed. Hausdorff Spectra in Functional Analysis. Springer, 2002.

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23

(Editor), Guillaume Brümmer, and Christopher Gilmour (Editor), eds. Papers in Honour of Bernhard Banaschewski. Springer, 2000.

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24

Oxtoby, John C. Measure and Category: A Survey of the Analogies between Topological and Measure Spaces. Springer, 2012.

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25

Measure and Category: A Survey of the Analogies between Topological and Measure Spaces. Springer, 2012.

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26

ing, Adámek Jiří, and Mac Lane Saunders 1909-, eds. Categorical topology and its relation to analysis, algebra and combinatorics: Prague, Czechoslovakia, 22-27 August 1988. Singapore: World Scientific Pub. Co., 1989.

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27

(Editor), Saunders MacLane, ed. Categorical Topology: And Its Relation to Analysis Algebra and Combinatorics : Prague, Czechoslovakia 22-27 August 1988. World Scientific Pub Co Inc, 1989.

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28

Oxtoby, John C. Measure and Category: A Survey of the Analogies between Topological and Measure Spaces (Graduate Texts in Mathematics). Springer, 1996.

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29

Hrushovski, Ehud, and François Loeser. A closer look at the stable completion. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0005.

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This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

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30

Behrens, Stefan, Boldizsar Kalmar, Min Hoon Kim, Mark Powell, and Arunima Ray, eds. The Disc Embedding Theorem. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198841319.001.0001.

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The disc embedding theorem provides a detailed proof of the eponymous theorem in 4-manifold topology. The theorem, due to Michael Freedman, underpins virtually all of our understanding of 4-manifolds in the topological category. Most famously, this includes the 4-dimensional topological Poincaré conjecture. Combined with the concurrent work of Simon Donaldson, the theorem reveals a remarkable disparity between the topological and smooth categories for 4-manifolds. A thorough exposition of Freedman’s proof of the disc embedding theorem is given, with many new details. A self-contained account of decomposition space theory, a beautiful but outmoded branch of topology that produces non-differentiable homeomorphisms between manifolds, is provided. Techniques from decomposition space theory are used to show that an object produced by an infinite, iterative process, which we call a skyscraper, is homeomorphic to a thickened disc, relative to its boundary. A stand-alone interlude explains the disc embedding theorem’s key role in smoothing theory, the existence of exotic smooth structures on Euclidean space, and all known homeomorphism classifications of 4-manifolds via surgery theory and the s-cobordism theorem. The book is written to be accessible to graduate students working on 4-manifolds, as well as researchers in related areas. It contains over a hundred professionally rendered figures.

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31

Wacquant, Loïc. Four Transversal Principles for Putting Bourdieu to Work. Edited by Thomas Medvetz and Jeffrey J. Sallaz. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199357192.013.30.

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Chapter abstract This chapter spotlights four transversal principles that undergird and animate Bourdieu’s research practice, and can fruitfully guide inquiry on any empirical front: the Bachelardian imperative of epistemological rupture and vigilance; the Weberian command to effect the triple historicization of the agent (habitus), the world (social space, of which field is but a subtype), and the categories of the analyst (epistemic reflexivity); the Leibnizian-Durkheimian invitation to deploy the topological mode of reasoning to track the mutual correspondences between symbolic space, social space, and physical space; and the Cassirer moment urging us to recognize the constitutive efficacy of symbolic structures. The chapter also flags three traps that Bourdieusian explorers of the social world should exercise special care to avoid: the fetishization of concepts, the seductions of “speaking Bourdieuse” while failing to carry out the research operations Bourdieu’s notions stipulate, and the forced imposition of his theoretical framework en bloc.

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