# Grothendieck 拓扑　`def.grothendieck-topology`
Grothendieck 拓扑与 site（Grothendieck Topology, Site）
layer 14 · 定义 · 层与拓扑 · 范畴论
[在星图里打开](../#n=def.grothendieck-topology)　·　[节点索引](../index.md)

范畴 $\mathcal{C}$ 上的 **Grothendieck 拓扑**是对每个 $X$ 指定一族**覆盖筛** $J(X)$，满足：
> 陈述续见 [nodes/def.grothendieck-topology.2.md](./def.grothendieck-topology.2.md)


## 它能推出什么 / 谁在用它
- ⇒ [`prop.covering-sieve-epi`](../nodes/prop.covering-sieve-epi.md) 覆盖筛即余积满射

- …另有出边，续页见 [nodes/def.grothendieck-topology.4.md](./def.grothendieck-topology.4.md)

## 为什么成立（入边，证明在 proofs/）
- …另有入边，续页见 [nodes/def.grothendieck-topology.3.md](./def.grothendieck-topology.3.md)

refs: Le Stum, An introduction to condensed mathematics, §3.1–3.2

外部：Wikipedia https://en.wikipedia.org/wiki/Grothendieck_topology · nLab https://ncatlab.org/nlab/show/Grothendieck+topology

> 说明见 `notes/def.grothendieck-topology.md`

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