2000/09/11 by Carlos Simpson, Simpson, Carlos
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #math.CT
paper · pdf · doi:10.48550/arxiv.math/0009107
not too long
arxiv created 2000/09/11 · openalex publication_date 2000/09/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give an explicit way of calculating the set of homotopy classes of morphisms from a Tamsamani n-category A to another one B. This calculation uses a Reedy-cofibrant cosimplicial resolution of A, using a new notion of ``free cofibration'' of n-precats. The free cofibrations of n-precats seem to be the analogue for n-categories of the Bousfield-Kan cofibrations in the theory of diagrams.