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Abstract

In this paper we use the theory of formal moduli problems developed by Lurie in order to study the space of formal deformations of a $k$-linear \infty$-category for a field $k$. Our main result states that if \mathcal{C}$ is a $k$-linear \infty$-category which has a compact generator whose groups of self-extensions vanish for sufficiently high positive degrees, then every formal deformation of \mathcal{C}$ has zero curvature and moreover admits a compact generator.