  The framework of templicial objects was put forth in arXiv:2302.02484v1 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 arXiv:2005.04778v3. 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.
