# Mathematical Sciences Research Institute

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# Seminar

HC-Special Seminar: 2-fold complete Segal spaces and Theta-2-spaces (Part 1) February 04, 2020 (11:00 AM PST - 12:00 PM PST)
Parent Program: Higher Categories and Categorification MSRI: Baker Board Room
Speaker(s) Lyne Moser (École Polytechnique Fédérale de Lausanne (EPFL))
Description No Description
Video
Abstract/Media

In this talk, I will start by presenting the notion of complete Segal spaces, due to Rezk. These model (∞,1)-categories. Then we will see two ways of extending this notion into models of (∞,2)-categories: 2-fold complete Segal spaces (due to Barwick) and Theta-2-spaces (due to Rezk). Finally, we will see that the two models are equivalent.

Title: 2-quasi-categories

Abstract: 2-quasi-categories are a model for (∞,2)-categories defined by Ara as the fibrant objects of a certain model structure on the category of $\Theta_2$-sets. In the first half of this talk, I will recall Ara's definition of 2-quasi-categories and Leinster's nerve construction, which embeds bicategories into 2-quasi-categories. In the second half, I will survey various constructions and results on 2-quasi-categories, including comparisons of 2-quasi-categories with Rezk's $\Theta_2$-spaces and with quasi-category-enriched Segal categories.

Bibliography:

- Dimitri Ara. Higher quasi-categories vs higher Rezk spaces. J. K-Theory 14 (2014), no. 3, 701--749.

- Alexander Campbell. A homotopy coherent cellular nerve for bicategories. Preprint, arXiv:1907.01999 (2019).

- Yuki Maehara. Inner horns for 2-quasi-categories. Adv. Math. 363 (2020).