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Título:
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Homotopy linear algebra
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Autor/a:
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Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew
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Otros autores:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions |
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Abstract:
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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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Abstract:
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Peer Reviewed |
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Materia(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
-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 |
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Derechos:
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Tipo de documento:
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Artículo - Versión presentada
Artículo |
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