# 带截面的覆盖上 Čech 零调　`prop.cech-section-vanishing`
命题：满射有截面时增广 Čech 复形同伦平凡
layer 17 · 命题 · 层上同调 · 同调代数
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设 $\mathcal{T}$ 是拓扑斯，$X_{0} \xrightarrow{\ p\ } X$ 是态射且**有截面** $s$（$p s = 1_{X}$）。记

$$X_{n} := X_{0} \times_{X} \cdots \times_{X} X_{0} \quad (n+1 \text{ 个因子}),$$
> 陈述续见 [nodes/prop.cech-section-vanishing.2.md](./prop.cech-section-vanishing.2.md)


## 它能推出什么 / 谁在用它
- ⇒ [`lem.covering-free-acyclic`](../nodes/lem.covering-free-acyclic.md) 覆盖给出的自由复形零调

## 为什么成立（入边，证明在 proofs/）
- …另有入边，续页见 [nodes/prop.cech-section-vanishing.3.md](./prop.cech-section-vanishing.3.md)

refs: Le Stum, An introduction to condensed mathematics, §7.3

> 说明见 `notes/prop.cech-section-vanishing.md`

引用：`prop.cech-section-vanishing`（内容 v0.9.0）· 条款见 [LICENSE.txt](../LICENSE.txt)