# Talk:Factorization system

WikiProject Mathematics (Rated Start-class, Low-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 Start Class
 Low Importance
Field:  Foundations, logic, and set theory

## 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') ${\displaystyle E\cap M}$ is exactly the class of isomorphisms of C.

because it is false : for example, in the category of sets, every function ${\displaystyle f:A\to B}$ can be factorized into an injection followed by a surjection, through the coproduct ${\displaystyle A+B}$, 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