# 有限表现对象　`def.finitely-presented`
有限表现（紧）对象（Finitely Presented Object）
layer 13 · 定义 · 预层与米田 · 范畴论
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对象 $X \in \mathcal{C}$ 叫**有限表现的**（也叫**紧的**，compact），如果可表函子

$$h^{X} = \operatorname{Hom}_{\mathcal{C}}(X, -)$$

**保滤过余极限**：对每个滤过图 $D$，$\operatorname{Hom}(X, \varinjlim D) \cong \varinjlim \operatorname{Hom}(X, D(-))$。

## 为什么成立（入边，证明在 proofs/）
- …另有入边，续页见 [nodes/def.finitely-presented.2.md](./def.finitely-presented.2.md)

refs: Le Stum, An introduction to condensed mathematics, §1.1–1.5

> 说明见 `notes/def.finitely-presented.md`

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