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We describe necessary and sufficient conditions for the hereditarity of the category algebra of an infinite EI category satisfying certain combinatorial assumptions. More generally, we discuss conditions such that the… Click to show full abstract
We describe necessary and sufficient conditions for the hereditarity of the category algebra of an infinite EI category satisfying certain combinatorial assumptions. More generally, we discuss conditions such that the left global dimension of a category algebra equals the maximal left global dimension of the endomorphism algebras of its objects, and classify its projective modules in this case. As applications, we completely classify transporter categories, orbit categories, and Quillen categories with left hereditary category algebras over a field.
Journal Title: Journal of Algebra
Year Published: 2022
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