# 正合因子让谱序列退化　`prop.derived-functor-exact-factor`
命题：$F$ 正合 $\implies R^{n}G(FK) \cong R^{n}(G \circ F)(K)$
layer 18 · 命题 · 过滤与谱序列 · 同调代数
[在星图里打开](../#n=prop.derived-functor-exact-factor)　·　[节点索引](../index.md)

设 $\mathcal{A} \xrightarrow{F} \mathcal{A}' \xrightarrow{G} \mathcal{A}''$ 是加法函子，满足 Grothendieck 谱序列的条件。若 $F$ 正合，则
> 陈述续见 [nodes/prop.derived-functor-exact-factor.2.md](./prop.derived-functor-exact-factor.2.md)


## 为什么成立（入边，证明在 proofs/）
- …另有入边，续页见 [nodes/prop.derived-functor-exact-factor.3.md](./prop.derived-functor-exact-factor.3.md)

refs: Le Stum, An introduction to condensed mathematics, Exercise 7.35

> 说明见 `notes/prop.derived-functor-exact-factor.md`

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