Dear Tony and Sasha,
I am writing to you as people who pointed my attention to the question
of the proper definition of curved (weak) A_\infty-algebras and their
(exotic) derived categories. This is to let you know about the recent
developments, which haven't been quite definitely verified yet, but
look correct and potentially relevant.
A short summary: curved A_\infty-coalgebras are better than curved
A_\infty-algebras in a number of respects. (But applicability to
any particular problems outside of the abstract Koszul duality
theory have not been considered, as always.)
( Read more... )