, Volume 8, Issue 1, pp 127-140

On the invariance and general cohomology comparison theorems

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Abstract

The Invariance Theorem of Gerstenhaber and Schack states that if $\mathbb A $ is a diagram of algebras then the subdivision functor induces a natural isomorphism between the Yoneda cohomologies of the category $\mathbb A $ - $\mathbf{mod }$ and its subdivided category $\mathbb A ^{\prime }$ - $\mathbf{mod }$ . In this paper we generalize this result and show that the subdivision functor is a full and faithful functor between two suitable derived categories of $\mathbb A $ - $\mathbf{mod }$ and $\mathbb A ^{\prime }$ - $\mathbf{mod }$ . This result combined with our work in Stancu (Hochschild cohomology and derived categories, PhD thesis, SUNY, Buffalo, 2006; J Homotopy Relat Struct 6(1):39–63, 2011), on the Special Cohomology Comparison Theorem, constitutes a generalization of Gerstenhaber and Schack’s General Cohomology Comparison Theorem (GCCT).

Communicated by Jim Stasheff.