# 同调的短正合列　`prop.cohomology-exact-sequence`
把同调夹在两个余核 / 核之间
layer 13 · 命题 · 同调与正合列 · 同调代数
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设 $K$ 是复形。则对每个 $k$ 有正合列

$$0 \longrightarrow H^{k}(K) \longrightarrow \operatorname{coker} d^{k-1} \longrightarrow \ker d^{k+1} \longrightarrow H^{k+1}(K) \longrightarrow 0$$

## 为什么成立（入边，证明在 proofs/）
- …另有入边，续页见 [nodes/prop.cohomology-exact-sequence.2.md](./prop.cohomology-exact-sequence.2.md)

refs: Le Stum, An introduction to condensed mathematics, §7.1–7.3

> 说明见 `notes/prop.cohomology-exact-sequence.md`

引用：`prop.cohomology-exact-sequence`（内容 v0.9.0）· 条款见 [LICENSE.txt](../LICENSE.txt)