2024/12/02 by Thibaut Benjamin, Benjamin, Thibaut
Mathematics · #18N65 #Advanced Topology and Set Theory #Algebraic structures and combinatorial models #Category Theory (math.CT) #F.2.1 #F.3.2 #FOS: Computer and information sciences #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic in Computer Science (cs.LO)
paper · pdf · doi:10.48550/arxiv.2412.01667
openalex publication_date 2024/12/02 · openalex created_date 2024/12/05 · openalex updated_date 2026/07/28
Finster and Mimram have defined a dependent type theory called CaTT, which describes the structure of omega-categories. Types in homotopy type theory with their higher identity types form weak omega-groupoids, so they are in particular weak omega-categories. In this article, we show that this principle makes homotopy type theory into a model of CaTT, by defining a translation principle that interprets an operation on the cell of an omega-category as an operation on higher identity types. We then illustrate how this translation allows to leverage several mechanisation principles that are available in CaTT, to reduce the proof effort required to derive results about the structure of identity types, such as the existence of an Eckmann-Hilton cell.