# 离散函子保直和　`prop.discrete-functor-coproduct`
命题：$\bigl(\bigoplus_{i} M_{i}\bigr)^{\mathrm{disc}} \cong \bigoplus_{i} M_{i}^{\mathrm{disc}}$
layer 18 · 命题 · 凝聚态阿贝尔群 · 凝聚态数学
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设 $(M_{i})_{i \in I}$ 是一族阿贝尔群。则

$$\Bigl(\bigoplus_{i \in I} M_{i}\Bigr)^{\mathrm{disc}} \;\cong\; \bigoplus_{i \in I} M_{i}^{\mathrm{disc}},$$
> 陈述续见 [nodes/prop.discrete-functor-coproduct.2.md](./prop.discrete-functor-coproduct.2.md)


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

refs: Le Stum, An introduction to condensed mathematics, Exercise 6.3

> 说明见 `notes/prop.discrete-functor-coproduct.md`

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