functor category

函子范畴

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

Translation evidence: Literature usage

Meaning in context

For small C and locally small D, the category whose objects are functors C→D and whose morphisms are natural transformations.

当 C 小且 D 局部小时，以 C→D 的函子为对象、自然变换为态射、逐分量合成为态射合成的范畴。

Example

For a discrete two-object CC, [C,Set][C,\mathbf{Set}] is the category of pairs of sets.

Usage and distinctions

The smallness of C ensures transformation collections are sets in this formulation.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§1.5, Definition 1.5.1 · 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，「函子范畴」，定义「函子范畴」及其后大小说明 · Checked 2026-10-14
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