202507210007

Tags : Category Theory

Separating and Coseparating sets

---

Definition

A separating set or a separator for a category $C$ is a set $\Phi$ of objects that can distinguish between distinct parallel morphism in the following sense: given $f,g:x\rightrightarrows y$, if $f\ne g$ then there exists some $h:c\to x$ with $c\in \Phi$ such that $fh\ne fg$. A coseparating set in $C$ is a separating set in $C^{\text{op}}$.

---

References