Differential calculus of Hochschild pairs for infinity-categories
Algebraic Geometry
2020-10-12 v3 Algebraic Topology
Quantum Algebra
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.
Keywords
Cite
@article{arxiv.1904.02359,
title = {Differential calculus of Hochschild pairs for infinity-categories},
author = {Isamu Iwanari},
journal= {arXiv preprint arXiv:1904.02359},
year = {2020}
}
Comments
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