Definition
Let C be a symmetric monoidal closed category. For any object A and, there exists a morphism
defined as the image by the bijection defining the monoidal closure, of the morphism
An object of the category C is called dualizing when the associated morphism is an isomorphism for every object A of the category C.
Equivalently, a *-autonomous category is a symmetric monoidal category C together with a functor such that for every object A there is a natural isomorphism, and for every three objects A, B and C there is a natural bijection
- .
The dualizing object of C is then defined by .
Read more about this topic: *-autonomous Category
Famous quotes containing the word definition:
“The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
—Ralph Waldo Emerson (1803–1882)
“Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
—Elaine Heffner (20th century)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)