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Title: Homotopy Linear Algebra
Authors: Tonks, Andrew P.
Kock, Joachim
Gálvez-Carrillo, Imma
First Published: 17-Oct-2017
Publisher: Cambridge University Press for Royal Society of Edinburgh
Citation: Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2017
Abstract: By homotopy linear algebra we mean the study of linear functors between slices of the ∞-category of ∞-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices into ∞-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 ∞-groupoids; we hope that they can also be of independent interest.
DOI Link: 10.1017/S0308210517000208
ISSN: 0308-2105
eISSN: 1473-7124
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2017, Royal Society of Edinburgh. Deposited with reference to the publisher’s open access archiving policy.
Description: The file associated with this record is under embargo until 6 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.
Appears in Collections:Published Articles, Dept. of Mathematics

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