# 单态射的切片刻画　`prop.slice-fully-faithful-mono`
命题：$f$ 单 $\iff$ $\mathcal{C}/Y \to \mathcal{C}/X$ 全忠实
layer 14 · 命题 · 单满、子对象与像 · 范畴论
[在星图里打开](../#n=prop.slice-fully-faithful-mono)　·　[节点索引](../index.md)

态射 $f : Y \to X$ 是**单态射** $\iff$ 沿 $f$ 的切片函子

$$\mathcal{C}/Y \longrightarrow \mathcal{C}/X, \qquad (A \to Y) \longmapsto (A \to Y \to X)$$
> 陈述续见 [nodes/prop.slice-fully-faithful-mono.2.md](./prop.slice-fully-faithful-mono.2.md)


## 为什么成立（入边，证明在 proofs/）
- …另有入边，续页见 [nodes/prop.slice-fully-faithful-mono.3.md](./prop.slice-fully-faithful-mono.3.md)

refs: Le Stum, An introduction to condensed mathematics, Exercise 1.32

> 说明见 `notes/prop.slice-fully-faithful-mono.md`

引用：`prop.slice-fully-faithful-mono`（内容 v0.9.0）· 条款见 [LICENSE.txt](../LICENSE.txt)