limit-preserving functor
nounUK /ˈlɪmɪt prɪˈzɜːvɪŋ ˈfʌŋktə/
US /ˈlɪmɪt prɪˈzɜrvɪŋ ˈfʌŋktər/
A limit-preserving functor is a rule that keeps special patterns called limits the same when it moves between math worlds.
In category theory, a limit-preserving functor maps every limit in one category to a limit in another.
RELATED WORDS
OTHER MEANINGS
2. A functor that commutes with small limits up to canonical isomorphism.
The forgetful functor from groups to sets is limit-preserving.
3. A functor preserving all finite limits, also called left exact.
A left exact functor is exactly a finitely limit-preserving functor.
4. In enriched category theory, a functor preserving weighted limits.
Enriched limit-preserving functors respect the enriched limit structure.