On the functoriality of cohomology of categories (Q2581277)

The cohomology \(H\) of \textit{H.-J. Baues} and \textit{G. Wirsching} [J. Pure Appl. Algebra 38, 187--211 (1985; Zbl 0587.18006)] of categories generalizes various known cohomology theories, such as Hochschild-Mitchell cohomology of categories, MacLane cohomology of rings, and cohomology with local coefficients of classifying spaces. It has been defined via the Baues-Wirsching complex \(F\). The paper under review considers the behaviour of \(H\) and of \(F\) under natural transformations between functors in the first variable. It is shown that \(F\) is a 2-functor into the 2-category of chain complexes. Localization and colocalization results are then derived.