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# The universal property of bispans

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

March 27, 2020 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Rune Haugseng (Norwegian University of Science and Technology (NTNU))
Location: MSRI: Online/Virtual
Tags/Keywords
• Bispans

• semirings

• $(\infty • 2)$-categories

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
Video

#### 11-Haugseng

Abstract

Commutative semirings can be described in terms of bispans of finite sets, meaning spans with an extra forward leg; if we instead take bispans in finite G-sets we get Tambara functors, which are the structure on $\pi_0$ of $G$-equivariant commutative ring spectra. Motivated by applications of the $\infty$-categorical upgrade of such descriptions to motivic and equivariant ring spectra, I will discuss the universal property of $(\infty,2)$-categories of bispans. I will focus on the simplest case of bispans in finite sets, where this gives a new construction of the semiring structure on a symmetric monoidal $\infty$-category whose tensor product commutes with coproducts. This is joint work with Elden Elmanto.

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#### 11-Haugseng

 H.264 Video 918_28234_8266_11-Haugseng.mp4
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