Differential Calculus of Hochschild Pairs for Infinity-Categories - Iwanari, Isamu (Symmetry, Integrability and Geometry: Methods and Applications, 2020)
In this paper, we provide a conceptual new construction of the algebraic structure on the pair of the Hochschild cohomology spectrum (cochain complex) and Hochschild homology spectrum, which is analogous to the structure of calculus on a manifold. This algebraic structure is encoded by a two-colored operad introduced by Kontsevich and Soibelman. We prove that for a stable idempotent-complete infinity-category, the pair of its Hochschild cohomology and homology spectra naturally admits the structure of an algebra over the operad. Moreover, we prove a generalization to the equivariant context.