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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.

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For the sake of clarity: what do you mean by a digraph? There are different conventions around. – user43208 Oct 12 '13 at 18:07
@user43208, is the edit sufficient? – goblin Oct 12 '13 at 18:10
Yes, although I'd not heard of that being one of the conventions! I'd heard of "set together with a relation" (no qualifier). – user43208 Oct 12 '13 at 18:12
@user43208, you can drop the reflexivity condition if you wish; I am not particularly attached to it. – goblin Oct 12 '13 at 18:18

The usual reference for "blank" category theory: Abstract and concrete categories (the Joy of cats), by Adámek, Herrlich, Strecker. In this case chapter 7.

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