Differential Calculus of Hochschild Pairs for Infinity-Categories

Isamu Iwanari

Symmetry, integrability and geometry: methods and applications, Tome 16 (2020)

Résumé

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.

Détail

Keywords: Hochschild cohomology, Hochschild homology, operad, $\infty$-category.

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