Homotopy theory and simplicial groupoids. (English) Zbl 0559.55023
The category
of simplicial groupoids is shown to admit the structure of a Quillen closed model category. The usual loop group functor on the category of reduced simplicial sets and the classifying complex functor on the category of simplicial groups are extended to functors G and \(\bar W\) between the category of simplicial sets and . The main result: The functors G and \(\bar W\) induce inverse homotopy equivalences of the corresponding hammock localizations.
Reviewer: H.Scheerer
MSC:
55U35 | Abstract and axiomatic homotopy theory in algebraic topology |
55U10 | Simplicial sets and complexes in algebraic topology |
55P10 | Homotopy equivalences in algebraic topology |
55R35 | Classifying spaces of groups and \(H\)-spaces in algebraic topology |
55P35 | Loop spaces |
18E35 | Localization of categories, calculus of fractions |
18G30 | Simplicial sets; simplicial objects in a category (MSC2010) |
18B40 | Groupoids, semigroupoids, semigroups, groups (viewed as categories) |