morphism in a category

态射

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

Other names / variants: arrow

Translation evidence: Literature usage

Meaning in context

An arrow with a specified source and target in a category, composable with other arrows when their endpoints match.

范畴中有指定来源和目标的箭头；端点相接时可与其他态射合成。

Example

A linear map k2→k3k^2\to k^3 is a morphism in Vectk\mathbf{Vect}_k.

Usage and distinctions

A morphism need not be a set function; an abstract category specifies its own arrows.

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 and Example 1.1.4 · 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，「范畴与态射」，def:category 中「态射」及 Hom-集 · Checked 2026-10-14
Edit source / propose a PRReport a correction

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.