functor

函子

Category Theory · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: covariant functor · 共变函子

Translation evidence: Literature usage

Meaning in context

An assignment of objects and arrows between categories that respects source, target, identities and composition.

范畴之间同时指定对象和态射的对应，并保持来源、目标、恒等态射和合成的结构。

Example

A↦A×AA\mapsto A\times A, f↦f×ff\mapsto f\times f, is a functor on sets.

Usage and distinctions

An object assignment alone is insufficient; preservation of identities must also be checked.

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Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§1.3, Definition 1.3.1 · 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，「函子与自然变换」，def:functor；其后「共变函子」 · Checked 2026-10-14
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