Cohomological results in monoid and category theory via classifying spaces
This work considers topological, homotopical and homological methodology in the study of monoids via the classifying space functor \(|\;|: {\mathcal C}at\to{\mathcal T}op\). An important adjunction \({\mathcal C}at\downarrow C\rightleftarrows{\mathcal C}at^{C^{op}}\) is described and used. Conditions are studied for the classifying space of a monoid to be equivalent to a finite-dimensional CW-complex. Spectral sequences associated to some functors give results (e.g., for the computation of the Euler characteristic of \(|C|\)). Informations are given to know when a surmorphism is a (co)homological equivalence.
scientific article; zbMATH DE number 802561