We construct spectral sequences in the framework of Baues–Wirsching cohomology and homology for functors between small categories and analyze particular cases including Grothendieck fibrations. We also give applications to more classical cohomology and homology theories including Hochschild–Mitchell cohomology and those studied before by Watts, Roos, Quillen and others.
Gálvez, I.; Neumann, F.; Tonks, A. André spectral sequences for Baues–Wirsching cohomology of categories. "Journal of pure and applied algebra", 30 Abril 2012, vol. 216, núm. 11, p. 2549-2561.