# The universal property of bispans

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

**Speaker(s):**Rune Haugseng (Norwegian University of Science and Technology (NTNU))

**Location:**SLMath: Online/Virtual

**Tags/Keywords**

Bispans

semirings

$(\infty

2)$-categories

**Primary Mathematics Subject Classification**

**Secondary Mathematics Subject Classification**

#### 11-Haugseng

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.

#### 11-Haugseng

H.264 Video | 918_28234_8266_11-Haugseng.mp4 |

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