In category theory, there's many variants on the notion of "monomorphism," such as:
- split monomorphism
- effective monomorphism
- regular monomorphism
- strong monomorphism
- extremal monomorphism
What are some good concrete examples for understanding the differences between these concepts? I'm especially interested categories of relational (as opposed to algebraic) structures, like the category of graphs, of digraphs, of posets, etc.
Edit. By digraph, I mean a set together with a reflexive relation. By graph, I mean a set together with a reflexive and symmetric binary relation. I'm not overly attached to the reflexivity stipulation; feel free to disregard it in either or both cases.