, Volume 8, Issue 1, pp 127-140
Date: 05 Oct 2012

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.