opposite category

反范畴

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

Translation evidence: Literature usage

Meaning in context

The category with the same objects as C, all arrows reversed, and composition performed in the reverse order.

对象与原范畴相同、态射方向反转、合成顺序相应反转的范畴。

Example

The opposite of the poset category 0<10<1 has its nonidentity arrow 1→01\to0.

Usage and distinctions

Reversing all arrows does not in general give a category isomorphic to the original.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§1.2 Duality · 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，「范畴与态射」，末尾「反范畴」定义 · Checked 2026-10-14
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