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.
