## A tale of two model structures

### Paula Verdugo Hernandez – 5 August 2020

I will be presenting joint work with Lyne Moser and Maru Sarazola, where we construct two model structures on the category of double categories and double functors. Both of these model structures share the distinctive feature of admitting a homotopically fully faithful functor from Lack's model structure on 2-categories to them -- this can be rephrased in vaguer terms as saying that they contain the homotopy theory of 2-categories. Moreover, both induce Lack's model structure through (some version of) the horizontal embedding $H:2Cat \to DblCat$. We will introduce these model structures together with their main properties, and discuss their similitudes and differences.

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