There are various definitions for cohomology groups of small categories, namely Cohomology as higher limits, Baues-Wirsching cohomology, and Thomason cohomology.

I will discuss the connections between the cohomology of categories and regular extensions of categories. I will show how different versions of LHS-spectral sequences can be constructed for regular extensions of categories, and discuss some applications of these spectral sequences to homology decompositions of p-local finite groups.