Stable infinity-categories with left and right complete t-structures have deformation functors that are formal E2-moduli problems determined by their Hochschild cohomology.
Gaitsgory, Ind-coherent sheaves, Mosc
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Hochschild cohomology and deformation theory of stable infinity-categories with t-structures
Stable infinity-categories with left and right complete t-structures have deformation functors that are formal E2-moduli problems determined by their Hochschild cohomology.