Two Model Structures for Double Categories

In this talk, I will present recent joint work with Lyne Moser and Paula Verdugo, where we construct two model structures for (the category of) double categories. Unlike the model structures previously present in the literature, both of our model structures contain the homotopy theory of 2-categories, and moreover, they both induce Lack’s model structure on 2- categories, through some version of the horizontal embedding $H: 2Cat \to DblCat$.
After recalling some preliminaries on double categories, 2-categories, and Lack’s model structure on 2Cat, we will introduce our two model structures on DblCat together with their main features, and discuss the pros and cons of each of them.