Varieties of simplicial groupoids. I: Crossed complexes
The paper is a contribution to the theory of algebraic models for homotopy types. \textit{W. G. Dwyer} and \textit{D. M. Kan} [Indag. Math. 46, 379-385 (1984; Zbl 0559.55023)] have shown that simplicial groupoids model all homotopy types completely. Partial models include crossed complexes which have been extensively studied by \textit{R. Brown} and \textit{P. J. Higgins} [J. Pure Appl. Algebra 47, 1-33 (1987; Zbl 0621.55009)]. In the paper, the simplicial groupoids that correspond to crossed complexes are shown to form a variety (epi-reflective subcategory) within the category of all simplicial groupoids and the corresponding verbal subgroupoid is identified.
scientific article; zbMATH DE number 1076655