On the invariance and general cohomology comparison theorems (Q1946127)

The general cohomology comparison theorem (GCCT) [\textit{M. Gerstenhaber} and \textit{S. D. Schack}, Trans. Am. Math. Soc. 310, No. 1, 135--165 (1988; Zbl 0706.16021)] asserts that the cohomology (and deformation theory) of a presheaf of unital associative algebras over a small category (called a diagram of algebras) is canonically isomorphic with the cohomology (and deformation theory) of a single algebra. The author uses his techniques developed in [Hochschild cohomology and derived categories. New York, Buffalo: University at Buffalo (PhD Thesis) (2006); ``On the cohomology comparison theorem'', J. Homotopy Relat. Struct. 6, No. 1, 39--63 (2011)] to prove a new result on the GCCT via a generalization of the invariance theorem [\textit{M. Gerstenhaber} and \textit{S. D. Schack}, Nato ASI Ser., Ser. C 247, 11--264 (1988; Zbl 0676.16022)].