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Generators in formal deformations of categories
- Part of
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- Journal:
- Compositio Mathematica / Volume 154 / Issue 10 / October 2018
- Published online by Cambridge University Press:
- 30 August 2018, pp. 2055-2089
- Print publication:
- October 2018
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- Article
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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.
