Deformations of quasi-categories in modules

Abstract

The framework of templicial objects was put forth in [30] in order to develop higher categorical concepts in the presence of enrichment. In particular, quasi-categories in modules constitute a subclass of templicial modules which may be considered as a kind of “weak dg-categories (concentrated in homologically positive degrees)” according to [29]. The main goal of the present paper is to initiate the deformation theory of templicial modules. In particular, we show that quasi-categories in modules are preserved under levelwise flat infinitesimal deformation.