{"paper":{"title":"Homotopy linear algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Andrew Tonks, Imma G\\'alvez-Carrillo, Joachim Kock","submitted_at":"2016-02-16T16:33:37Z","abstract_excerpt":"By homotopy linear algebra we mean the study of linear functors between slices of the $\\infty$-category of $\\infty$-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices into $\\infty$-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 $\\infty$-groupoids; we hope that they can also be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05082","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}