Cubical approach to derived functors

Patchkoria, Irakli

doi:10.4310/hha.2012.v14.n1.a7

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Construction Of a Projective Resolution1

Cubical Sets In Algebraic Topology1

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Cited by 2 publications

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“…1 Relations between morphisms of the cube category involved in the proof that the functor Zh I k / ZD k is projective were used by A. Swiatec [55] for study of cubical objects in the abelian category and I. Pachkoria [53] to study pseudo-cubical objects of an idempotently complete preadditive category.…”

Section: Construction Of a Projective Resolutionmentioning

confidence: 99%

Homology and cohomology of cubical sets with coefficients in systems of objects

Husainov¹

2022

Preprint

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This paper continues the research of the author on the homology of cubical and semi-cubical sets with coefficients in systems. The main result is the theorem that the homology of cubical sets with coefficients in contravariant systems in an Abelian category with exact coproducts is isomorphic to the left satellites of a colimit functor. It allowed proving a number of new assertions presented in this paper about homology and cohomology of cubical sets with coefficients in systems, including homology and cohomology with coefficients in local systems.

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Section: Construction Of a Projective Resolutionmentioning

confidence: 99%

Homology and cohomology of cubical sets with coefficients in systems of objects

Husainov¹

2022

Preprint

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“…G. Maltsiniotis in [Mal09] showed that up to homotopy, connections correct the realisation problem. Patchkoria in [Pat12] gave a cubical approach to derived functors. Cubical sets have analogously been used for work on motives, see [Vez14], and the references there 10 .…”

Section: Cubical Sets In Algebraic Topologymentioning

confidence: 99%

Modelling and computing homotopy types: I

Brown

2018

Indagationes Mathematicae

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The aim of this article is to explain a philosophy for applying the 1-dimensional and higher dimensional Seifert-van Kampen Theorems, and how the use of groupoids and strict higher groupoids resolves some foundational anomalies in algebraic topology at the border between homology and homotopy. We explain some applications to filtered spaces, and special cases of them, while a sequel will show the relevance to n-cubes of pointed spaces.

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Cubical approach to derived functors

Cited by 2 publications

References 14 publications

Homology and cohomology of cubical sets with coefficients in systems of objects

Homology and cohomology of cubical sets with coefficients in systems of objects

Modelling and computing homotopy types: I

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