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.
CitationProceedings of the Royal Society of Edinburgh: Section A Mathematics, 2017
Author affiliation/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics
VersionAM (Accepted Manuscript)
Published inProceedings of the Royal Society of Edinburgh: Section A Mathematics
PublisherCambridge University Press for Royal Society of Edinburgh
NotesThe 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.