Curved A-infinity-categories : Adjunction and Homotopy (original) (raw)

We develop a theory of curved A ∞-categories around equivalences of their module categories. This allows for a uniform treatment of curved and uncurved A ∞-categories which generalizes the classical theory of uncurved A ∞-algebras. Furthermore, the theory is sufficiently general to treat both Fukaya categories and categories of matrix factorizations, as well as to provide a context in which unitification and categorification of pre-categories can be carried out. Our theory is built around two functors: the adjoint algebra functor U e and the functor Q *. The bulk of the paper is dedicated to proving crucial adjunction and homotopy theorems about these functors. In addition, we explore the non-vanishing of the module categories and give a precise statement and proof the folk result known as "Positselski-Kontsevich vanishing".

Sign up for access to the world's latest research.

checkGet notified about relevant papers

checkSave papers to use in your research

checkJoin the discussion with peers

checkTrack your impact