Diagonal tensor algebra and naïve liftings

The notion of naïve lifting of differential graded (DG) modules along certain DG algebra extensions was introduced by the authors for the purpose of studying problems in homological commutative algebra that involve self-vanishing of Ext. Our goal in this paper is to deeply study naïve lifting property using the diagonal tensor algebra. Our main result provides several characterizations of naïve liftability of DG modules under certain Ext vanishing conditions. As an application, we affirmatively answer a question posed by the authors regarding a specific characterization of naïve liftability.