Why call "monic" an injective function?

Question

In Golan's book "The Linear Algebra a Beginning Graduate Student Ought to Know", the author calls monic a function that assigns different elements to different elements. Is there a reason for that?

Answer 1

That is because the monics in the category of sets are exactly the injective functions. Therefore one can do that, but I think one should not (at least in that context) as it is only confusing.

There is something called category theory where one can define some more general notion of injective maps which are called monics/monomorphisms. Depending on the category, they might not be injective though (and it does not even always make sense to ask whether they are injective because they do not have to be maps and the objects do not necessarily have elements).