Varieties of simplicial groupoids I: Crossed complexes

✍ Scribed by P.J. Ehlers; T. Porter

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 785 KB
• Volume: 120
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(96)00038-2

✦ Synopsis

It is usual to use algebraic models for homotopy types. Simplicial groupoids provide such a model. Other partial models include the crossed complexes of Brown and Higgins. In this paper, the simplicial groupoids that correspond to crossed complexes are shown to form a variety within the category of all simplicial groupoids and the corresponding verbal subgroupoid is identified.