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Sibirsk. Mat. Zh., 2012, Volume 53, Number 4, Pages 943–950 (Mi smj2375)  

The global dimension of polynomial categories in partially commuting variables

A. A. Khusainov

Komsomolsk-on-Amur State Technical University, Komsomolsk-on-Amur

Abstract: We study the global dimension of the category of objects of an abelian category carrying an action of a free partially commutative monoid. We calculate this dimension in the case that the abelian category has infinite coproducts and enough projectives. Previously the author solved the same problem for abelian categories with exact coproducts.

Keywords: cohomology of small categories, free partially commutative monoid, trace monoid, global dimension.

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English version:
Siberian Mathematical Journal, 2012, 53:4, 757–762

Bibliographic databases:

UDC: 512.66
Received: 29.03.2011

Citation: A. A. Khusainov, “The global dimension of polynomial categories in partially commuting variables”, Sibirsk. Mat. Zh., 53:4 (2012), 943–950; Siberian Math. J., 53:4 (2012), 757–762

Citation in format AMSBIB
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\by A.~A.~Khusainov
\paper The global dimension of polynomial categories in partially commuting variables
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 4
\pages 943--950
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\jour Siberian Math. J.
\yr 2012
\vol 53
\issue 4
\pages 757--762
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