Relationship With Monoidal Functors
If there is a monoidal functor from a monoidal category M to a monoidal category N, then any category enriched over M can be reinterpreted as a category enriched over N. Every monoidal category M has a monoidal functor M(I, –) to the category of sets, so any enriched category has an underlying ordinary category. In many examples (such as those above) this functor is faithful, so a category enriched over M can be described as an ordinary category with certain additional structure or properties.
Read more about this topic: Enriched Category
Famous quotes containing the word relationship:
“Every relationship that does not raise us up pulls us down, and vice versa; this is why men usually sink down somewhat when they take wives while women are usually somewhat raised up. Overly spiritual men require marriage every bit as much as they resist it as bitter medicine.”
—Friedrich Nietzsche (1844–1900)