A universal property of the monoidal 2-category of cospans of finite linear orders and surjections

TL;DR

This paper establishes a universal property of a specific monoidal 2-category involving cospans of finite linear orders and surjections, characterizing its foundational algebraic structures.

Contribution

It proves that this monoidal 2-category is the universal setting with an object having semigroup and cosemigroup structures satisfying a 2-dimensional separable algebra condition.

Findings

Identifies the universal property of the monoidal 2-category

Characterizes the algebraic structures involved

Provides a foundational framework for related categorical constructions

Abstract

We prove that the monoidal 2-category of cospans of finite linear orders and surjections is the universal monoidal category with an object X with a semigroup and a cosemigroup structures, where the two structures satisfy a certain 2-dimensional separable algebra condition.