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