Closed model structures for algebraic models of n-types. Journal of Pure and Applied Algebra

Abstract

In this paper we give a general method to obtain a closed model structure, in the sense of Quillen, on a category related to the category of simplicial groups by a suitable adjoint situation. Applying this method, categories of algebraic models of connected types such as those of crossed modules of groups (2-types), 2-crossed modules of groups (3-types) or, in general. n-hypercrossed complexes of groups ((n + I)-types), as well as that of n-simplicial groups (all types), inherit such a closed model structure.