Homotopy linear algebra

Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks

Research output: Contribution to journalArticleResearchpeer-review

13 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)293-325
Number of pages33
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Issue number2
Publication statusPublished - 1 Apr 2018


  • duality
  • homotopy cardinality
  • homotopy finiteness
  • infinity-groupoids
  • linear algebra


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