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:
“He serveth the servant,
The brave he loves amain;
He kills the cripple and the sick,
And straight begins again.
For gods delight in gods,
And thrust the weak aside;
To him who scorns their charities,
Their arms fly open wide.”
—Ralph Waldo Emerson (1803–1882)
“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)