Lax Functors, Cospans, and the Center Construction

TL;DR

This paper extends the classical center construction to a lax functor in the category of rings, utilizing Lurie's universal construction, and explores its applications to Morita categories and cospans.

Contribution

It introduces a lax functorial version of the center construction for rings, building on Lurie's universal construction, and applies it to Morita categories and cospans.

Findings

Classical center is not functorial, but can be extended to a lax functor.

Constructs lax functors to Morita categories and cospans.

Provides a new perspective on the functoriality of the center in algebra.

Abstract

The center construction is not (classically) functorial. In this note, we specialize a universal construction of Jacob Lurie to the category of rings and upgrade the classical center to a lax functor. In particular, we find lax functors to the Morita category and the category of cospans.