publication . Preprint . 2010

The Invariance and the General CCT Theorems

Stancu, Alin;
Open Access English
  • Published: 11 Aug 2010
Abstract
The \begin{it} Invariance Theorem \end{it} of M. Gerstenhaber and S. D. 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 $\mathbb{A}'$-$\mathbf{mod}$. 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 $\mathbb{A}'$-$\mathbf{mod}$. This result combined with our work in [5] and [6], on the $Special$ $Cohomology$ $Comparison$ $Theorem$, constitutes a generalizati...
Subjects
arXiv: Mathematics::Category TheoryMathematics::K-Theory and HomologyMathematics::Algebraic Topology
free text keywords: Mathematics - Category Theory
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ALIN STANCU ExtiA,k(M, N) ≃ M orDk−(A−mod)(M•, N•[i]) ExtiA′,k(M′, N′) ≃ M orDk−(A′−mod)(M′•, N′•[i]) [1] S. I. Gelfand and Yu. I. Manin, “Methods of Homological Algebra”, Springer Verlag (1996).

[2] M. Gerstenhaber and S. D. Schack, “Algebraic Cohomology and Deformation Theory”, Deformation Theory of Algebras and Structures and Applications, Kluwer, Dordrecht (1988) 11-264.

[3] M. Gerstenhaber and S. D. Schack, “The Cohomology of Presheaves of Algebras: Presheaves over a Partially Ordered Set”, Trans. Amer. Math. Soc. 310 (1988) 135-165.

[4] S. MacLane, “Homology ”, Spinger-Verlag, Berlin, (1967).

[5] A. A. Stancu, “Hochschild Coheomology and Derived Categories”, SUNY at Buffalo Ph.D. thesis, (2006).

[6] A. A. Stancu, “On the Cohomology Comparison Theorem”, Journal of Homotopy and Related Structures, to appear.

E-mail address: stancu alin1@colstate.edu

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