Differential calculus of Hochschild pairs for infinity-categories

Abstract

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 algebra over the operad. Moreover, we prove a generalization to the equivariant context.

minor change

References in corpus (4)

• Higher Topos Theory
• Formality of the homotopy calculus algebra of Hochschild (co)chains
• The homotopy fixed points of the circle action on Hochschild homology
• Period mappings for noncommutative algebras