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

[Moved Online] (∞, n)-categories, factorization homology, and algebraic K-theory March 23, 2020 - March 27, 2020

March 27, 2020 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Viktoriya Ozornova (Max-Planck-Institut für Mathematik)
Location: MSRI: Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC



In collaboration with Martina Rovelli.

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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H.264 Video 918_28226_8265_10-Ozornova.mp4
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