representable functor

可表函子

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Translation evidence: Literature usage

Meaning in context

A set-valued functor naturally isomorphic to Hom(-,A) in the contravariant case, or Hom(A,-) in the covariant case.

反变情形自然同构于 Hom(-,A)、或共变情形自然同构于 Hom(A,-) 的集合值函子。

Example

On sets, B↦BAB\mapsto B^A is represented covariantly by AA.

Usage and distinctions

A family of bijections without naturality is not a representation.

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Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§2.1, Definition 2.1.4 · Checked 2026-10-14

Translation sources

  1. 李文威 — 代数学方法，第一卷（作者源码）第2章，「可表函子」，定义 def:representable-functor · Checked 2026-10-14
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