strict 2-category
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In category theory in mathematics, a 2-category is a category with "morphisms between morphisms", called 2-morphisms. A basic example is the category Cat of all (small) categories, where a 2-morphism is a natural transformation between functors.
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18 sectionsContents
- Definitions
- A strict 2-category
- As a category enriched over Cat
- A weak 2-category
- Examples
- Category of small categories
- Grpd
- Ord
- Boolean monoidal category
- Coherence theorem
- Duskin nerve
- Functors and natural transformations
- Related notion: double category
- See also
- Footnotes
- References
- Further reading
- External links
In category theory in mathematics, a 2-category is a category with "morphisms between morphisms", called 2-morphisms. A basic example is the category Cat of all (small) categories, where a 2-morphism is a natural transformation between functors.
The concept of a strict 2-category was first introduced by Charles Ehresmann in his work on enriched categories in 1965. The more general concept of bicategory (or weak 2-category), where composition of morphisms is associative only up to a 2-isomorphism, was introduced in 1967 by Jean Bénabou.