gistfile1.txt

<lkuper> is it equivalent to say that a function is invertible and that it's a bijection?
<shachaf> Yes.
<lkuper> ok :)
<shachaf> But you have to be careful if you have "functions" between more complicated structures.
<shachaf> In which case there might be more requirements on the inverse. But not with plain old functions.
<lkuper> ah. by ""functions" between more complicated structures", do you mean, like, some other kind of morphism?
<lkuper> (I'm dealing with plain old functions here, but curious)
<shachaf> Right.
<shachaf> E.g. you might care that the inverse of a continuous function is continuous, or something.
<lkuper> I see.  so, maybe another way to say this is that, when dealing with sets, it turns out bijectivity and invertibility coincide, but invertibility is a more general concept and applies to fancier kinds of objects too
<lkuper> thanks for the insight :)
<shachaf> It kind of depends on how you define words, really.
<lkuper> haha, yeah
<shachaf> Probably you'd say "isomorphism" if you wanted to be really clear that you're talking about morphisms in some other category.
<shachaf> And you'd say "bijection" if you wanted to be clear that you just mean something between sets.