Weak Factorization Systems
Suppose e and m are two morphisms in a category C. Then e has the left lifting property with respect to m (resp. m has the right lifting property with respect to e) when for every pair of morphisms u and v such that ve=mu there is a morphism w such that the following diagram commutes. The difference with orthogonality is that w is not necessarily unique.
A weak factorization system (E, M) for a category C consists of two classes of morphisms E and M of C such that :
- The class E is exactly the class of morphisms having the left lifting property wrt the morphisms of M.
- The class M is exactly the class of morphisms having the right lifting property wrt the morphisms of E.
- Every morphism f of C can be factored as for some morphisms and .
Read more about this topic: Factorization System
Famous quotes containing the words weak and/or systems:
“The great fact was the land itself, which seemed to overwhelm the little beginnings of human society that struggled in its sombre wastes. It was from facing this vast hardness that the boy’s mouth had become so bitter; because he felt that men were too weak to make any mark here, that the land wanted to be let alone, to preserve its own fierce strength, its peculiar, savage kind of beauty, its uninterrupted mournfulness.”
—Willa Cather (1873–1947)
“The skylines lit up at dead of night, the air- conditioning systems cooling empty hotels in the desert and artificial light in the middle of the day all have something both demented and admirable about them. The mindless luxury of a rich civilization, and yet of a civilization perhaps as scared to see the lights go out as was the hunter in his primitive night.”
—Jean Baudrillard (b. 1929)