If is a small category, then a right –module is a contravariant functor from into abelian groups. The abelian category of right –modules has enough projective and injective objects, and the groups provide the basic cohomology theory for –modules. We introduce, for each integer , an approach for a level– cohomology theory for –modules by defining cohomology groups , , which are the focus of this article. Applications to the homotopy classification of braided and symmetric –fibred categorical groups and their homomorphisms are given.
María Calvo. Antonio M Cegarra. Nguyen T Quang. "Higher cohomologies of modules." Algebr. Geom. Topol. 12 (1) 343 - 413, 2012. https://doi.org/10.2140/agt.2012.12.343