The finite generation conjecture for cohomology of finite tensor categories is equivalent to finite generation of Hochschild cohomology for the endomorphism algebras of projective generators.
Venkov,Cohomology algebras for some classifying spaces(Russian), Dokl
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On the cohomology of finite tensor categories
The finite generation conjecture for cohomology of finite tensor categories is equivalent to finite generation of Hochschild cohomology for the endomorphism algebras of projective generators.