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Title:
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Thomason cohomology of categories
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Author:
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Gálvez Carrillo, Maria Immaculada; Neumann, Frank; Tonks, Andrew
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
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Abstract:
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We investigate cohomology and homology theories of categories with general coefficients given by functors on simplex categories first studied by Thomason. These generalize Baues–Wirsching cohomology and homology of a small category, and coincide with Gabriel–Zisman cohomology and homology of the simplicial nerve of the category. Thus Baues–Wirsching cohomology of categories is seen to be a special case of simplicial cohomology. We analyze naturality and functoriality properties of these theories and construct associated spectral sequences for functors between small categories. |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de categories; àlgebra homològica
-Homology theory
-Algebra, Homological
-K-theory
-Homologia
-K-teoria
-Àlgebra homològica
-Classificació AMS::18 Category theory; homological algebra::18G Homological algebra
-Classificació AMS::18 Category theory; homological algebra::18D Categories with structure
-Classificació AMS::55 Algebraic topology::55U Applied homological algebra and category theory |
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Rights:
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Document type:
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Article - Submitted version
Article |
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