Bounded t-deformations of a bounded t-dg-category are equivalent to dg-deformations of its category of derived injectives, and HH^n classifies them for n at least 2.
Faisceaux pervers,
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Deformations of triangulated categories with t-structures via derived injectives
Bounded t-deformations of a bounded t-dg-category are equivalent to dg-deformations of its category of derived injectives, and HH^n classifies them for n at least 2.