# Homotopy Invariants of Braided Commutative Algebras and the Deligne Conjecture for Finite Tensor Categories

@inproceedings{Schweigert2022HomotopyIO, title={Homotopy Invariants of Braided Commutative Algebras and the Deligne Conjecture for Finite Tensor Categories}, author={Christoph Schweigert and Lukas Woike}, year={2022} }

It is easy to ﬁnd algebras T ∈ C in a ﬁnite tensor category C that naturally come with a lift to a braided commutative algebra T ∈ Z ( C ) in the Drinfeld center of C . In fact, any ﬁnite tensor category has at least two such algebras, namely the monoidal unit I and the canonical end (cid:82) X ∈C X ⊗ X ∨ . Using the theory of braided operads, we prove that for any such algebra T the homotopy invariants, i.e. the derived morphism space from I to T , naturally come with the structure of a di…

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