The homotopy category of pseudofunctors and translation cohomology (Q995634)

Homotopy categories, track categories are categories enriched by groupoids. We are in the 2-category of abelian track categories, pseudofunctors and pseudonatural transformations. The translation cohomology is introduced in order to classify endomorphisms in the previous 2-category. The obstruction theory here developed is defined in the Baues-Wirsching cohomology of categories. Some element of a third cohomology of \({\mathcal A}\) vanishes if and only if there exists a pseudofunctor \({\mathcal A}\to {\mathcal B}\) satisfying some property. An interpretation of this obstruction is given in terms of exact sequences for functors and linear extensions of categories.