Homotopy linear algebra
By homotopy linear algebra we mean the study of linear functors between slices of the 8-category of 8-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices into 8-categories to model the duality between vector spaces and profinite-d...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/112830 |
| Acesso em linha: | https://hdl.handle.net/2117/112830 https://dx.doi.org/10.1017/S0308210517000208 |
| Access Level: | acceso abierto |
| Palavra-chave: | Homotopy theory Algebra, Homological Algebraic topology duality homotopy cardinality homotopy finiteness infinity-groupoids linear algebra Topologia algebraica Homotopia, Teoria d' Àlgebra homològica Classificació AMS::55 Algebraic topology::55P Homotopy theory Classificació AMS::15 Linear and multilinear algebra matrix theory Classificació AMS::18 Category theory homological algebra::18G Homological algebra Classificació AMS::46 Associative rings and algebras::46A Topological linear spaces and related structures Classificació AMS::37 Dynamical systems and ergodic theory::37F Complex dynamical systems Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica |
| Resumo: | By homotopy linear algebra we mean the study of linear functors between slices of the 8-category of 8-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices into 8-categories to model the duality between vector spaces and profinite-dimensional vector spaces, and set up a global notion of homotopy cardinality à la Baez, Hoffnung and Walker compatible with this duality. We needed these results to support our work on incidence algebras and Möbius inversion over 8-groupoids; we hope that they can also be of independent interest. |
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