category

范畴

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

Translation evidence: Literature usage

Meaning in context

Objects and directed morphisms with specified sources, targets, associative composition and a two-sided identity at each object.

由对象及有指定来源、目标的态射组成，配有结合的合成和各对象上的双侧恒等态射的结构。

Example

A poset gives a category with one arrow x→yx\to y exactly when x≤yx\leq y.

Usage and distinctions

The arrows are part of the definition: the same objects with different allowed arrows give different categories.

Read the encyclopedia explanation

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§1.1, Definition 1.1.1 · 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，「范畴与态射」，定义 def:category · Checked 2026-10-14
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