Talk:Factorization system

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

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

(2') is exactly the class of isomorphisms of C.

because it is false : for example, in the category of sets, every function 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