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Homotopy Linear Algebra

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journal contribution
posted on 17.11.2017, 10:41 by Andrew P. Tonks, Joachim Kock, Imma Gálvez-Carrillo
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.

History

Citation

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2017

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

AM (Accepted Manuscript)

Published in

Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Publisher

Cambridge University Press for Royal Society of Edinburgh

issn

0308-2105

eissn

1473-7124

Acceptance date

14/06/2016

Copyright date

2017

Available date

17/04/2018

Publisher version

https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/homotopy-linear-algebra/8E584127A7FB28AE5520B6604C7FC3C2

Notes

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.

Language

en