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 words relationship with and/or relationship:
“Henry David Thoreau, who never earned much of a living or sustained a relationship with any woman that wasn’t brotherly—who lived mostly under his parents’ roof ... who advocated one day’s work and six days “off” as the weekly round and was considered a bit of a fool in his hometown ... is probably the American writer who tells us best how to live comfortably with our most constant companion, ourselves.”
—Edward Hoagland (b. 1932)
“If the relationship of father to son could really be reduced to biology, the whole earth would blaze with the glory of fathers and sons.”
—James Baldwin (1924–1987)