Generators in formal deformations of categories

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.