# 上同调的函子性　`prop.cohomology-functoriality`
命题：$H^{n}(X', M^{\bullet}) \to H^{n}\bigl(f^{-1}(X'), f^{-1}M^{\bullet}\bigr)$
layer 18 · 命题 · 层上同调 · 同调代数
[在星图里打开](../#n=prop.cohomology-functoriality)　·　[节点索引](../index.md)

设 $f : \mathcal{T} \to \mathcal{T}'$ 是拓扑斯态射。则对 $X' \in \mathcal{T}'$ 与复形 $M^{\bullet}$，存在**典范映射**
> 陈述续见 [nodes/prop.cohomology-functoriality.2.md](./prop.cohomology-functoriality.2.md)


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

refs: Le Stum, An introduction to condensed mathematics, Exercise 7.54

> 说明见 `notes/prop.cohomology-functoriality.md`

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