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 human face is a weak guarantee; yet it deserves some consideration. And if I had to whip the wicked, I would do so more severely to those who belied and betrayed the promises that nature had implanted on their brows; I would punish malice more harshly when it was hidden under a kindly appearance.”
—Michel de Montaigne (1533–1592)
“Not out of those, on whom systems of education have exhausted their culture, comes the helpful giant to destroy the old or to build the new, but out of unhandselled savage nature, out of terrible Druids and Berserkirs, come at last Alfred and Shakespeare.”
—Ralph Waldo Emerson (1803–1882)