Herscovich, Estanislao2024-01-122024-01-122024-01-12202310.4310/HHA.2023.v25.n1.a15https://infoscience.epfl.ch/handle/20.500.14299/202918We provide a new description of the complex computing the Hochschild homology of an -unitary -algebra as a derived tensor product such that: (1) there is a canonical morphism from it to the complex computing the cyclic homology of that was introduced by Kontsevich and Soibelman, (2) this morphism induces the map in the well-known SBI sequence, and (3) is canonically isomorphic to the space of morphisms from to in the derived category of -bimodules. As direct consequences we obtain previous results of Cho and Cho–Lee, as well as the fact that Koszul duality establishes a bijection between (resp., almost exact) -Calabi–Yau structures and (resp., strong) homotopy inner products, extending a result proved by Van den Bergh.dg (co)algebra, -algebraCalabi–YauKoszul dualitytext::journal::journal article::research article