Hochschild cohomology and deformation theory of stable infinity-categories with t-structures

TL;DR

This paper establishes that Hochschild cohomology controls the deformation theory of stable infinity-categories with left complete t-structures, providing a new perspective on their structural flexibility.

Contribution

It demonstrates that Hochschild cohomology governs deformations of stable infinity-categories with t-structures, linking cohomological invariants to deformation theory.

Findings

Hochschild cohomology governs deformation theory of such categories

Deformation theory is characterized by Hochschild cohomology in this setting

Provides a new framework connecting cohomology and t-structure deformations

Abstract

Given a stable presentable infinity-category $\mathcal{E}$ equipped with a left complete t-structure, we prove that its Hochschild cohomology governs the deformation theory of $\mathcal{E}$ with respect to left complete t-structures.