| definiendum | ${\bf C}$ in $\mathrm{it}$ |
| exists | $F$ … equivalence of categories $({\bf C}, {\bf D})$ |
| for all | $f:\mathrm{Mor}_{\bf D}$ |
| exists | $A\in{\bf D}$ |
| postulate | $f=1_A$ |
A discrete category either has no non-identity arrows or at least is equivalent to such a category.
The discrete categories with $n$ objects are denoted ${\bf n}$.
nLab: Discrete category
Wikipedia: Discrete category