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We describe necessary and sufficient conditions for the hereditarity of thecategory algebra of an infinite EI category satisfying certain combinatorialassumptions. More generally, we discuss conditions such that the left globaldimension of a category algebra equals the maximal left global dimension of theendomorphism algebras of its objects, and classify its projective modules inthis case. As applications, we completely classify transporter categories,orbit categories, and Quillen categories with left hereditary category algebrasover a field.

Sufficient and necessary conditions for hereditary of infinite category algebras