# Leray 谱序列　`thm.leray-spectral-sequence`
定理：$E^{p,q}_{2} = H^{p}\bigl(X', R^{q}f_{*}M^{\bullet}\bigr) \implies H^{p+q}\bigl(f^{-1}X', M^{\bullet}\bigr)$
layer 18 · 定理 · 层上同调 · 同调代数
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设 $f : \mathcal{T} \to \mathcal{T}'$ 是拓扑斯态射、$X' \in \mathcal{T}'$、$M^{\bullet}$ 是 $\mathcal{T}$ 里的阿贝尔群复形。则存在谱序列
> 陈述续见 [nodes/thm.leray-spectral-sequence.2.md](./thm.leray-spectral-sequence.2.md)


## 为什么成立（入边，证明在 proofs/）
- …另有入边，续页见 [nodes/thm.leray-spectral-sequence.3.md](./thm.leray-spectral-sequence.3.md)

refs: Le Stum, An introduction to condensed mathematics, Exercise 7.56

> 说明见 `notes/thm.leray-spectral-sequence.md`

引用：`thm.leray-spectral-sequence`（内容 v0.9.0）· 条款见 [LICENSE.txt](../LICENSE.txt)