Michael Shulman
eso-generator

A family $F$ of objects in a 2-category $K$ with finite limits is said to be eso-generating if for any ff $m:A\to B$ in $K$, if every morphism $G\to B$ for $G\in F$ factors through $m$, then $m$ is an equivalence.

Examples

• When $K$ is a 1-category, this reduces to the usual notion of strong generator?.

• In $\mathrm{Cat}$, the singleton family $\{1\}$ is eso-generating.