TY - MGZN
AU - Galvez, M.
AU - Kock, J.
AU - Tonks, A.
T2 - Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Y1 - 2018
VL - 148
IS - 2
SP - 293
EP - 325
DO - 10.1017/S0308210517000208
UR - https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/homotopy-linear-algebra/8E584127A7FB28AE5520B6604C7FC3C2
AB - 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.
TI - Homotopy linear algebra
ER -