Homology groups of cubical sets
type: Item
instance of: scholarly article
title: Homology groups of cubical sets
zbMATH Open document ID: 1439.18012
published in: Applied Categorical Structures
publication date: 2019-06-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/1801.03324
review text: The author studies homology groups of cubical sets with coeficients in contravariant systems of abelian groups. The main result shows that these groups are isomorphic to the values of left derived functors of the colimit functor on this contravariant system.
reviewed by: Jiří Rosický
Mathematics Subject Classification ID: 18G10
Mathematics Subject Classification ID: 55U15
zbMATH DE Number: 7069460
zbMATH Keywords: cubical set
zbMATH Keywords: cubical homology
zbMATH Keywords: derived functor
author: Ahmet A. Khusainov
describes a project that uses: ChainCon
MaRDI profile type: Publication
OpenAlex ID: W2964266197
arXiv ID: 1801.03324
cites work: Q4304740
cites work: Nonabelian algebraic topology. Filtered spaces, crossed complexes, cubical homotopy groupoids. With contributions by Christopher D. Wensley and Sergei V. Soloviev
cites work: Acyclic Models
cites work: Algebraic topology and concurrency
cites work: Q5580926
cites work: Thomason cohomology of categories
cites work: Q3625520
cites work: Q4707052
cites work: Discrete Morse theoretic algorithms for computing homology of complexes and maps
cites work: Homological dimension theory of small categories
cites work: On the homology of small categories and asynchronous transition systems
cites work: The homology of partial monoid actions and Petri nets
cites work: Categorical homotopy theory
cites work: Computational homology
cites work: Computing homology
cites work: Homotopy equivalence of coverings and the spectral sequence of a fibration
cites work: Comparing dimensions of a small category
cites work: Cubical homology and the Leech dimension of free partially commutative monoids
cites work: Q3545562
cites work: Homology of left non-degenerate set-theoretic solutions to the Yang-Baxter equation
cites work: Homology
cites work: Q4215784
cites work: Basiserweiterung in der Homologie kleiner Kategorien
cites work: Homology of categories and exactness of direct limits
cites work: Computation of cubical homology, cohomology, and (co)homological operations via chain contraction
cites work: Homologie singulière des espaces fibrés. Applications
Wikidata QID: Q128904997
DOI: 10.1007/S10485-018-9550-2
description: scientific article