2015/06/11 by Jeffrey Armstrong, Armstrong, Jeffrey, Patrick Clarke +1
Mathematics · #16D90 #53D37 #57T30 #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.AG #math.CT #math.SG #msc:16D90 #msc:53D37 #msc:57T30
paper · pdf · doi:10.48550/arxiv.1506.03711
This version is organized slightly differently than version 1. In addition we have improved our treatment of Positselski-Kontsevich vanishing, and included proof that the our notion of equivalent curved A-infinity categories agrees with the classical one when the curvature is zero
arxiv created 2015/10/15 · arxiv updated 2015/10/16
We develop a theory of curved A-infinity-categories around equivalences of their module categories. This allows for a uniform treatment of curved and uncurved A-infinity-categories which generalizes the classical theory of uncurved A-infinity 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 Ue 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 result known as "Positselski-Kontsevich vanishing".