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Sibirskii Matematicheskii Zhurnal, 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
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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.
Received: 29.03.2011
English version:
Siberian Mathematical Journal, 2012, Volume 53, Issue 4, Pages 757–762
DOI: https://doi.org/10.1134/S0037446612040179
Bibliographic databases:
Document Type: Article
UDC: 512.66
Language: Russian
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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