[002G] Definition 4.3·a (Separating family for a category).

Given an ordinary category $E$, a set-indexed family $\prn{s\Sub{i}}\Sub{i\in I}$ of $E$-objects is called a small separating family for $E$ when, assuming that for all $i\in I$ and all $u:s_i\to x$ we have $u;f=u;g$, we then have $f=g$.