# 预层范畴　`def.presheaf-cat`
预层范畴（Category of Presheaves）
layer 10 · 定义 · 预层与米田 · 范畴论
[在星图里打开](../#n=def.presheaf-cat)　·　[节点索引](../index.md)

$\mathcal{C}$ 上全体预层以自然变换为态射，组成范畴

$$\widehat{\mathcal{C}} := \operatorname{Hom}(\mathcal{C}^{\mathrm{op}}, \mathbf{Set})$$

## 为什么成立（入边，证明在 proofs/）
- [`def.natural-transformation`](../nodes/def.natural-transformation.md) 自然变换：用到了定义 自然变换　[proofs/def-dep.nat-presheafcat.md](../proofs/def-dep.nat-presheafcat.md)
- [`def.functor`](../nodes/def.functor.md) 函子：用到了定义 函子　[proofs/def-dep.functor-presheafcat.md](../proofs/def-dep.functor-presheafcat.md)

## 它能推出什么 / 谁在用它
- …另有出边，续页见 [nodes/def.presheaf-cat.2.md](./def.presheaf-cat.2.md)

refs: Le Stum, An introduction to condensed mathematics, §1.1–1.5

> 说明见 `notes/def.presheaf-cat.md`

引用：`def.presheaf-cat`（内容 v0.9.0）· 条款见 [LICENSE.txt](../LICENSE.txt)