Talk:Factorization system

Examples?

As far as I can tell, literally the only examples given here are the classes of injections and surjections in the category of sets. I think the page might be better with some more examples. vivacissamamente (talk) 01:34, 26 February 2014 (UTC)

Removed

In the section "Equivalent definition", I have removed the part

The condition (2) above can be shown to be equivalent to the condition

(2') $E\cap M$ is exactly the class of isomorphisms of C.

because it is false : for example, in the category of sets, every function $f:A\to B$ can be factorized into an injection followed by a surjection, through the coproduct $A+B$, and a function which is both an injection and a surjection is an isomorphism, but it is not true that (Injections, Surjections) is a factorization system. It is a weak factorization system, whereas (Surjections, Injections) is a factorization system. breckes 2 October 2007