Embedding 2-categories into (\infty,2)-categories

In collaboration with Viktoriya Ozornova.

We will present how, by means of a suitable nerve construction, the established homotopy theory of strict 2-categories is fully recovered in the model of (\infty,2)-categories given by 2-complicial sets.

In the first talk, we will review the basics of 2-complicial sets, and we will introduce the nerve construction. We will then discuss some of its formal properties, and explain that it induces an embedding of the Lack's homotopy theory of 2-categories into the homotopy theory of Verity's 2-complicial sets.

In the second talk, we will give an explicit combinatorial description of the nerve which we can use to study many relevant homotopical properties. For instance, we will show that the nerve commutes up to equivalence with many relevant constructions, such as certain pushouts or suspensions.

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