Speaker: Arne Mertens – University of Antwerp
Abstract: I will introduce a candidate model for ($\infty$-)categories weakly enriched in simplicial objects, based on the Joyal model for quasi-categories. The main idea is to replace the category of simplicial sets by a category of certain colax monoidal functors, inspired by a result of Leinster and Bacard’s work on Segal enriched categories. We call them “templicial objects” and define quasi-categories analogously to the classical situation. In the linear case, equipping these with some extra structure, they become equivalent to non-negatively graded dg-categories through a lift of Lurie’s dg-nerve. At present, no analogue of Joyal’s model structure exists for templicial objects, but I will outline some partial results in that direction. This is joint work with Wendy Lowen.