## Discrete category

### Collection

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 | $f=1_A$ |

### Discussion

#### Idea

A discrete category either has no non-identity arrows or at least is equivalent to such a category.

#### Terminology

The discrete categories with $n$ objects are denoted ${\bf n}$.

#### Reference

nLab: Discrete category

Wikipedia: Discrete category