Mappings of bar constructions (Q1072162)

The author generalizes Quillen's theorems A and B [\textit{D. G. Quillen}, Lect. Notes Math. 341, 85-147 (1973; Zbl 0292.18004)] describing homotopy properties of the induced mapping Bf: B\({\mathcal C}\to B{\mathcal C}'\) where \(f: {\mathcal C}\to {\mathcal C}'\) is a functor and B is the classifying space functor to bar constructions in the category Top of topological spaces. Further generalizations in the spirit of the author [J. Pure Appl. Algebra 33, 163-207 (1984; Zbl 0542.57036)] where for instance Top is replaced by a suitable category with homotopy are announced.