Monic

If a composition (of morphisms) is monic then, by theorem, the pre-composite of it is monic as well.

It is often convenient to view a monic arrow i#58;A#92;rightarrowtailC, defined in Chapter 1, as showing that A is a copy of a part of C, and that i maps the copy on to that part. For example, in Set, the monic arrows are the one-to-one functions and, clearly, if i is one-to-one then A is a copy of a subset of C, namely of the image of i.