Relevant bibliographies by topics / Algebraic topology – Applied homological algebra and category theory – Applied homological algebra and category theory

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books

Academic literature on the topic 'Algebraic topology – Applied homological algebra and category theory – Applied homological algebra and category theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Algebraic topology – Applied homological algebra and category theory – Applied homological algebra and category theory.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Algebraic topology – Applied homological algebra and category theory – Applied homological algebra and category theory"

1

Song, Weiling, Tiwei Zhao, and Zhaoyong Huang. "Homological Dimensions Relative to Special Subcategories." Algebra Colloquium 28, no. 01 (2021): 131–42. http://dx.doi.org/10.1142/s1005386721000122.

Full text
Abstract:
Let [Formula: see text] be an abelian category, [Formula: see text] an additive, full and self-orthogonal subcategory of [Formula: see text] closed under direct summands, [Formula: see text] the right Gorenstein subcategory of [Formula: see text] relative to [Formula: see text], and [Formula: see text] the left orthogonal class of [Formula: see text]. For an object [Formula: see text] in [Formula: see text], we prove that if [Formula: see text] is in the right 1-orthogonal class of [Formula: see text], then the [Formula: see text]-projective and [Formula: see text]-projective dimensions of [Fo
APA, Harvard, Vancouver, ISO, and other styles
2

ALB, ALINA, and MIHAIL URSUL. "A FEW HOMOLOGICAL CHARACTERIZATIONS OF COMPACT SEMISIMPLE RINGS." Journal of Algebra and Its Applications 04, no. 05 (2005): 539–49. http://dx.doi.org/10.1142/s0219498805001411.

Full text
Abstract:
Fix any compact ring R with identity. We associate to R the following categories of topological R-modules: (i) R𝔇 (𝔇R) the category of all discrete topological left (right) R-modules; (ii) Rℭ (ℭR) the category of all compact left (right) R-modules. We have introduced the following notions (analogous with classical notions of module theory): (i) the tensor product [Formula: see text] of A ∈ ℭR and B ∈Rℭ ([Formula: see text] has a structure of a compact Abelian group); (ii) a topologically semisimple module; (iii) a compact topologically flat module. We give a characterization of compact semisim
APA, Harvard, Vancouver, ISO, and other styles
3

BARAKAT, MOHAMED, and MARKUS LANGE-HEGERMANN. "AN AXIOMATIC SETUP FOR ALGORITHMIC HOMOLOGICAL ALGEBRA AND AN ALTERNATIVE APPROACH TO LOCALIZATION." Journal of Algebra and Its Applications 10, no. 02 (2011): 269–93. http://dx.doi.org/10.1142/s0219498811004562.

Full text
Abstract:
In this paper we develop an axiomatic setup for algorithmic homological algebra of Abelian categories. This is done by exhibiting all existential quantifiers entering the definition of an Abelian category, which for the sake of computability need to be turned into constructive ones. We do this explicitly for the often-studied example Abelian category of finitely presented modules over a so-called computable ring R, i.e. a ring with an explicit algorithm to solve one-sided (in)homogeneous linear systems over R. For a finitely generated maximal ideal 𝔪 in a commutative ring R, we show how solvin
APA, Harvard, Vancouver, ISO, and other styles
4

WEI, REN, and ZHONGKUI LIU. "A QUILLEN MODEL STRUCTURE APPROACH TO HOMOLOGICAL DIMENSIONS OF COMPLEXES." Journal of Algebra and Its Applications 13, no. 03 (2013): 1350106. http://dx.doi.org/10.1142/s0219498813501065.

Full text
Abstract:
In this paper, we first give an alternative characterization of the derived functor Ext via the Quillen model structure on the category of complexes induced by a given cotorsion pair [Formula: see text] in the category of modules, then based on this, we consider homological dimensions of complexes related to [Formula: see text]. As applications, we extend Gorenstein projective dimension of homologically bounded below complexes (in the sense of Christensen and coauthors) to unbounded complexes whenever R is Gorenstein. Moreover, we extend Stenström's FP-injective dimension from modules to compl
APA, Harvard, Vancouver, ISO, and other styles
5

EICK, BETTINA, and DAVID J. GREEN. "COCHAIN SEQUENCES AND THE QUILLEN CATEGORY OF A COCLASS FAMILY." Journal of the Australian Mathematical Society 102, no. 2 (2016): 185–204. http://dx.doi.org/10.1017/s1446788716000185.

Full text
Abstract:
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.
APA, Harvard, Vancouver, ISO, and other styles
6

Zhang, Chao. "On the representation type of subcategories of derived categories." Journal of Algebra and Its Applications 18, no. 05 (2019): 2050032. http://dx.doi.org/10.1142/s0219498820500322.

Full text
Abstract:
Let [Formula: see text] be a finite-dimensional [Formula: see text]-algebra. In this paper, we mainly study the representation type of subcategories of the bounded derived category [Formula: see text]. First, we define the representation type and some homological invariants including cohomological length, width, range for subcategories. In this framework, we provide a characterization for derived discrete algebras. Moreover, for a finite-dimensional algebra [Formula: see text], we establish the first Brauer–Thrall type theorem of certain contravariantly finite subcategories [Formula: see text]
APA, Harvard, Vancouver, ISO, and other styles
7

Tu, Junwu. "Matrix factorizations via Koszul duality." Compositio Mathematica 150, no. 9 (2014): 1549–78. http://dx.doi.org/10.1112/s0010437x14007295.

Full text
Abstract:
AbstractIn this paper we prove a version of curved Koszul duality for $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathbb{Z}/2\mathbb{Z}$-graded curved coalgebras and their cobar differential graded algebras. A curved version of the homological perturbation lemma is also obtained as a useful technical tool for studying curved (co)algebras and precomplexes. The results of Koszul duality can be applied to study the category of m
APA, Harvard, Vancouver, ISO, and other styles
8

NEHANIV, CHRYSTOPHER LEV. "ALGEBRAIC CONNECTIVITY." International Journal of Algebra and Computation 01, no. 04 (1991): 445–71. http://dx.doi.org/10.1142/s0218196791000316.

Full text
Abstract:
Let [Formula: see text] be a type of algebra in the sense of universal algebra. By defining singular simplices in algebras and emulating singular [co] homology, we introduce for each variety, pseudo-variety, and divisional class V of type [Formula: see text], a homology and cohomology theory which measure the V-connectivity of type-[Formula: see text] algebras. Intuitively, if we were to think of an algebra as a space and subalgebras which lie in V as simplices, then V-connectivity describes the failure of subalgebras to lie in V, i.e., it describes the "holes" in this space. These [co]homolog
APA, Harvard, Vancouver, ISO, and other styles
9

Gao, Zenghui, and Wan Wu. "Gorenstein flat modules relative to injectively resolving subcategories." Journal of Algebra and Its Applications, February 24, 2021, 2250099. http://dx.doi.org/10.1142/s0219498822500992.

Full text
Abstract:
Let [Formula: see text] be an injectively resolving subcategory of left [Formula: see text]-modules. We introduce and study [Formula: see text]-Gorenstein flat modules as a common generalization of some known modules such as Gorenstein flat modules (Enochs, Jenda and Torrecillas, 1993), Gorenstein AC-flat modules (Bravo, Estrada and Iacob, 2018). Then we define a resolution dimension relative to the [Formula: see text]-Gorensteinflat modules, investigate the properties of the homological dimension and unify some important properties possessed by some known homological dimensions. In addition,
APA, Harvard, Vancouver, ISO, and other styles
10

Becerril, Víctor. "Relative global Gorenstein dimensions." Journal of Algebra and Its Applications, July 6, 2021, 2250208. http://dx.doi.org/10.1142/s0219498822502085.

Full text
Abstract:
Let [Formula: see text] be an abelian category. In this paper, we investigate the global [Formula: see text]-Gorenstein projective dimension [Formula: see text], associated to a GP-admissible pair [Formula: see text]. We give homological conditions over [Formula: see text] that characterize it. Moreover, given a GI-admissible pair [Formula: see text], we study conditions under which [Formula: see text] and [Formula: see text] are the same.
APA, Harvard, Vancouver, ISO, and other styles

Dissertations / Theses on the topic "Algebraic topology – Applied homological algebra and category theory – Applied homological algebra and category theory"

1

(8740848), Virgil Chan. "An Explicit Formula for the Loday Assembly." Thesis, 2020.

Find full text
Abstract:
We give an explicit description of the Loday assembly map on homotopy groups when restricted to a subgroup coming from the Atiyah-Hirzebruch spectral sequence. This proves and generalises a formula about the Loday assembly map on the first homotopy group that originally appeared in work of Waldhausen. Furthermore, we show that the Loday assembly map is injective on the second homotopy groups for a large class of integral group rings. Finally, we show that our methods can be used to compute the universal assembly map on homotopy.
APA, Harvard, Vancouver, ISO, and other styles

Books on the topic "Algebraic topology – Applied homological algebra and category theory – Applied homological algebra and category theory"

1

Modern classical homotopy theory. American Mathematical Society, 2011.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
2

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. American Mathematical Society, 2014.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
3

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. American Mathematical Society, 2015.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
4

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. American Mathematical Society, 2015.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
5

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

Find full text
APA, Harvard, Vancouver, ISO, and other styles
6

Persistence theory: From quiver representations to data analysis. American Mathematical Society, 2015.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
7

1974-, Zomorodian Afra J., ed. Advances in applied and computational topology: American Mathematical Society Short Course on Computational Topology, January 4-5, 2011, New Orleans, Louisiana. American Mathematical Society, 2012.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
8

Dundas, B. I. The Local Structure of Algebraic K-Theory. Springer London, 2013.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
9

Loday, Jean-Louis. Algebraic Operads. Springer Berlin Heidelberg, 2012.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
10

Center for Mathematics at Notre Dame and American Mathematical Society, eds. Toplogy and field theories: Center for Mathematics at Notre Dame, Center for Mathematics at Notre Dame : summer school and conference, Topology and field theories, May 29-June 8, 2012, University of Notre Dame, Notre Dame, Indiana. American Mathematical Society, 2014.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography