Closed model structures for algebraic models of n-types Original Research Article

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 + l)-types), as well as that of n-simplicial groups (all types), inherit such a closed model structure.