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Title:
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Homotopy linear algebra
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Author:
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Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew
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Other authors:
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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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arXiv:1602.05082 [math.CT] |
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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 \`a la Baez-Hoffnung-Walker compatible with this duality. We needed these results to support our work on incidence algebras and M\ |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
-Homotopy theory
-Algebra, Homological
-Algebraic topology
-Algebraic Topology
-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 |
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Rights:
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Document type:
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Article - Draft
Report |
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