Homotopy linear algebra
Tipo de documentoArtículo
Fecha de publicación2018-04
Condiciones de accesoAcceso abierto
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 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 8-groupoids; we hope that they can also be of independent interest.
CitaciónGalvez, M., Kock, J., Tonks, A. Homotopy linear algebra. "Proceedings of the Royal Society of Edinburgh: Section A Mathematics", Abril 2018, Volume 148, Issue 2, p. 293-325