An application of A-infinity obstruction theory to representation theory

The existence and uniqueness of enhancements for triangulated categories is an old problem in algebra
and topology, e.g. the stable homotopy category has a unique enhancement up to Quillen equivalence
(Schwede), the derived category of a Grothendieck category too (Canonaco-Stellari), etc. These examples
have a common feature: they are large categories. Triangulated categories of finite type over a perfect
field arise commonly in representation theory. We will show how to use the homotopy theory of operads
in order to prove that these triangulated categories have unique enhancements. This applies to Amiot's
non-standard 1-Calabi-Yau categories in positive characteristic.