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.
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Original Russian Text Copyright © 2012 Khusainov A.A.
The author was supported by the program of the Strategic Development of the State Institutions for Higher Professional Education (Grant 2011-PR-054).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 4, pp. 943–950, July–August, 2012.
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Khusainov, A.A. The global dimension of polynomial categories in partially commuting variables. Sib Math J 53, 757–762 (2012). https://doi.org/10.1134/S0037446612040179
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DOI: https://doi.org/10.1134/S0037446612040179