Obstruction to naive liftability of DG modules

Abstract

The notion of naive liftability of DG modules is introduced in [9] and [10]. In this paper, we study the obstruction to naive liftability along extensions $A\to B$ of DG algebras, where $B$ is projective as an underlying graded $A$-module. We show that the obstruction to naive liftability of a semifree DG $B$-module $N$ is a certain cohomology class in Ext${}_B^1(N,N{\otimes }_{B}J)$, where $J$ is the diagonal ideal. Our results on obstruction class enable us to give concrete examples of DG modules that do and do not satisfy the naive lifting property.

References in corpus (1)

• Naive liftings of DG modules