Homotopy linear algebra
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 \`a la Baez-Hoffnung-Walker compatible with this duality. We needed these results to support our work on incidence algebras and M\"obius inversion over -groupoids; we hope that they can also be of independent interest.
Cite
@article{arxiv.1602.05082,
title = {Homotopy linear algebra},
author = {Imma Gálvez-Carrillo and Joachim Kock and Andrew Tonks},
journal= {arXiv preprint arXiv:1602.05082},
year = {2018}
}
Comments
32 pages. This paper is one of six papers that formerly constituted the long manuscript arXiv:1404.3202. v2: slight notation changes and expository improvements. Final version, to appear in Proc Royal Soc. Edinburgh A