# 保有限积的函子作用于代数对象　`prop.functor-preserves-monoid-objects`
命题：$F$ 保有限积 $\implies F$ 诱导 $\mathrm{Mon}(\mathcal{C}) \to \mathrm{Mon}(\mathcal{D})$
layer 15 · 命题 · 范畴里的代数结构 · 范畴论
[在星图里打开](../#n=prop.functor-preserves-monoid-objects)　·　[节点索引](../index.md)

若 $F : \mathcal{C} \to \mathcal{D}$ **保有限积**（含终对象），则它把
> 陈述续见 [nodes/prop.functor-preserves-monoid-objects.2.md](./prop.functor-preserves-monoid-objects.2.md)


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

refs: Le Stum, An introduction to condensed mathematics, Exercise 1.53

> 说明见 `notes/prop.functor-preserves-monoid-objects.md`

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