Differential calculus of hochschild pairs for infinity-categories

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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.

Original languageEnglish
Article number097
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Publication statusPublished - 2020


  • Hochschild cohomology
  • Hochschild homology
  • Operad
  • ∞-category


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