Also known as covariant functor, contravariant functor
In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic objects (such as the fundamental group) are associated to topological spaces, and maps between these algebraic objects are associated to continuous maps between spaces. Nowadays, functors are used throughout modern mathematics to relate various categories. Thus, functors are important in every area of mathematics where category theory is applied.
In the Vinony graph
Vinony's link graph records 601 inbound references to 函子, and connects out to universal property, strict 2-category and continuous function.
It is catalogued under the topic Functors.
Vinony links it to 29 Wikipedia language editions.
Wikidata facts
- Subclass of
- function
- Part of
- category theory
- Image
- Commutative diagram of a functor.svg
Show 6 more facts
- topic's main category
- Category:Functors
- discoverer or inventor
- Saunders Mac Lane
- Commons category
- Functors
- studied by
- category theory
- different from
- function object
- maintained by WikiProject
- WikiProject Mathematics
Sources (2)
via Wikidata · CC0
Article · 中文
在範疇論中，函子是範疇間的一類映射。函子也可以解釋為內的態射。 函子首先現身於代數拓撲學，其中拓撲空間的連續映射給出相應的代數对象（如基本群、同調群或上同調群）的代數同態。在當代數學中，函子被用來描述各種範疇間的關係。「函子」（英文：Functor）一詞借自哲學家魯道夫·卡爾納普的用語。卡爾納普使用「函子」這一詞和函數之間的相關來類比謂詞和性質之間的相關。對卡爾納普而言，不同於當代範疇論的用法，函子是個語言學的詞彙。對範疇論者來說，函子則是個特別類型的函數。
Abstract from DBpedia / Wikipedia · CC BY-SA