Thomason cohomology of categories
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 sim...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/19437 |
| Acceso en línea: | https://hdl.handle.net/2117/19437 https://dx.doi.org/10.1016/j.jpaa.2013.02.005 |
| Access Level: | acceso abierto |
| Palabra clave: | Homology theory Algebra, Homological K-theory Homologia K-teoria Àlgebra homològica Classificació AMS::18 Category theory homological algebra::18G Homological algebra homological algebra::18D Categories with structure Classificació AMS::55 Algebraic topology::55U Applied homological algebra and category theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de categories àlgebra homològica |
| Sumario: | 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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