2022/01/06 by Claudio Pisani, Pisani, Claudio
Mathematics · #Advanced Topics in Algebra #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2201.01967
openalex publication_date 2022/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a fibration in groupoids d : D -> I, we define a fibered multicategory as a particular functor p : M -> I, where M has the same objects as D, and its arrows a : X -> Y should be thought of as families of arrows in the multicategory, indexed by pY. The key axiom extends the reindexing of objects, given by d, to a reindexing of arrows in M along pullback squares in I. When D is included in M, in an appropriate sense, one gets again fibered categories. In this context, cartesian fibered multicategories are defined and studied in a natural way.