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.
Xu,Hochschild and ordinary cohomology rings of small categories, Adv
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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.