V2EX colimit

Colimit

释义 Definition

colimit(余极限):范畴论中的一个概念,表示把一个“图式”(一组对象与态射构成的结构)以最通用的方式“拼接/合并”成一个对象;它是某种“极限(limit)”概念的对偶(dual)。常见的 colimit 例子包括 coproduct(余积)pushout(推出)coequalizer(余等化子)、以及(在合适范畴中)direct limit / inductive limit(直极限/归纳极限)

发音 Pronunciation

/kolmt/

例句 Examples

A coproduct is a kind of colimit.
余积是一类余极限。

The colimit of this diagram identifies elements according to the morphisms, producing a universal object that factors every compatible cocone.
这个图式的余极限会按照态射把元素进行识别并“粘合”,从而得到一个具有泛性质的对象:任何与之相容的余锥都能唯一地经由它分解。

词源 Etymology

co- 表示“对偶、反向”(在数学中常用来表示与某概念取对偶),limit 指“极限”。因此 co-limit 字面意思就是“与极限对偶的概念”。该术语在 20 世纪中期随现代范畴论的发展而定下来,用来统一描述“合并/拼接”型的泛构造。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Categories for the Working Mathematician Saunders Mac Lane(系统介绍极限与余极限等基本概念)
  • Category Theory Steve Awodey(教材中多处使用 colimit 解释范畴论的“拼接”构造)
  • Basic Category Theory Tom Leinster(入门书,讨论常见 colimit:余积、推出等)
  • Sheaves in Geometry and Logic Saunders Mac Lane & Ieke Moerdijk(在层与拓扑/逻辑背景下频繁使用 colimit)
  • Locally Presentable and Accessible Categories J. Adámek & J. Rosick(更高阶文本,系统使用各类 colimit 条件)
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