摘要：
第一部分摘要: For a finite EI category, we prove that its category algebra is Gorenstein if and only if the given category is projective; and that its category algebra is 1-Gorenstein if and only if the given category is free and projective.

第二部分摘要: For a finite projective EI category, the stable category of Gorenstein-projective modules over the category algebra is tensor triangle equivalent to the singularity category of the category algebra. If in addition the category is free, we construct a maximal Cohen-Macaulay approximation of the trivial module, which is exactly the tensor identity of the above stable category. In this case, we prove that Gorenstein-projective modules are closed under the tensor product if and only if each morphism in the given category is a monomorphism.

邀请人：周国栋