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 1-category for a eld k. Our
main result states that if C is a k-linear 1-category which has a compact generator
whose groups of self-extensions vanish for suciently high positive degrees, then every
formal deformation of C has zero curvature and moreover admits a compact generator.