V2EX coproduct

Coproduct

定义 Definition

coproduct(余积 / 对偶积):范畴论中的一个基本构造,是“product(积)”的对偶概念。直观上,它把若干对象“合并”为一个对象,并带有从各个对象指向该合并对象的典范态射,满足一个普遍性质(universal property)。在许多具体范畴里,coproduct 常对应“不交并”或“直和”。

发音 Pronunciation (IPA)

/koprdkt/

例句 Examples

In Set, the coproduct of two sets is their disjoint union.
集合范畴 Set 中,两个集合的 coproduct 是它们的不交并

The coproduct is defined by a universal mapping property, so any pair of maps out of the components factors uniquely through it.
coproduct 由一个泛映射性质刻画,因此从各个组成部分射出的任意一对映射,都会唯一地经由 coproduct 诱导分解。

词源 Etymology

co- 表示“与……对应/共同”,product 表示“积”;合在一起强调它与 product(积) 互为对(dual)。该术语主要在 20 世纪的范畴论发展中固定下来,用来命名“积”的对偶构造。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Categories for the Working Mathematician(Saunders Mac Lane)
  • Category Theory(Steve Awodey)
  • Basic Category Theory(Tom Leinster)
  • Topoi: The Categorical Analysis of Logic(Robert Goldblatt)
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