CT (Category theory)
This is the same as Baues-Wirsching cohomology
Baues: Homotopy types (e), section 5.
See Generalov in Handbook of Algebra vol 1, in Various folder under ALGEBRA
arXiv:1102.5756 Cohomology of exact categories and (non-)additive sheaves from arXiv Front: math.KT by Dmitry Kaledin, Wendy Lowen We use (non-)additive sheaves to introduce an (absolute) notion of Hochschild cohomology for exact categories as Ext’s in a suitable bisheaf category. We compare our approach to various definitions present in the literature.
arXiv:1002.1650 The bordism version of the h-principle from arXiv Front: math.CT by Rustam Sadykov In view of the Segal construction each category with operation gives rise to a cohomology theory. We show that similarly each open stable differential relation R determines cohomology theories k^* of solutions and h^* of stable formal solutions of R. We prove that k^* and h^* are equivalent under a mild condition
For example, in the case of the covering differential relation our theorem is equivalent to the Barratt-Priddy-Quillen theorem asserting that the direct limit of classifying spaces B\Sigma_n of permutation groups \Sigma_n of finite sets of n elements is homology equivalent to each path component of the infinite loop space \Omega^{\infty}S^{\infty}.
http://ncatlab.org/nlab/show/cohomology+of+a+category
nLab page on Cohomology of categories