[formal-methods] Injective, Surjective, and Bijective functions

[d p chang]

Crutcher Dunnavant <crutcher at gmail.com> writes:

> As to the issue at hand, it seems trivial to say that injection
> abstracts to monomorphism and surjection abstracts to
> epimorphism. Awody's book (Category Theory) makes this claim on page
> 25. What I haven't seen anywhere, and I've looked, is a claim that it
> is incorrect to say that injection and surjection are synonyms for
> their more general concepts.

your last sentence has me really confused. for example, i think of
surjection as (w/o the notation that i'm too lazy to check the emacs
input mode for):

 f is surjective iff, there exists x in X, for all y in Y, such that
 f(x) = y
 

are you saying that:

 - we have a context in which surjective means something else?

 - epimorphism isn't exactly surjection?

 - something else that i didn't understand

\p

---
The liberty of the press is most generally approved when it takes
liberties with the other fellow, and leaves us alone. - Edgar Watson Howe