contravariant functor

反变函子

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

Translation evidence: Literature usage

Meaning in context

A functor Cᵒᵖ→D, viewed as an assignment from C reversing the direction of arrows.

从反范畴 Cᵒᵖ 到 D 的函子；视作从 C 出发的对应时，它反转态射方向。

Example

For fixed AA, Hom⁡(−,A)\operatorname{Hom}(-,A) sends f:X→Yf:X\to Y to precomposition Hom⁡(Y,A)→Hom⁡(X,A)\operatorname{Hom}(Y,A)\to\operatorname{Hom}(X,A).

Usage and distinctions

Reversing arrows changes the composition law: F(gf)=F(f)F(g).

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§1.3, Definition 1.3.5 · 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 后「反变函子」 · Checked 2026-10-14
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