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types of morphisms

Defines: 
monomorphism, epimorphism, bimorphism, retraction, section, coretraction, isomorphism, inverse morphism, split monomorphism, split epimorphism, epimorphic extension, epimorphic monomorphism
Type of Math Object: 
Definition
Major Section: 
Reference

Mathematics Subject Classification

18A05 no label found

Comments

I've added this entry despite the fact that some of these notions are already defined somewhere in PM. In my opinion it's good to have these definitions gathered in one place.

They can be found e.g. in
http://planetmath.org/encyclopedia/AbelianCategory.html
http://planetmath.org/encyclopedia/Epi.html
http://planetmath.org/encyclopedia/Monic.html

I've seen that epimorphism or monomorphism often redirects to
http://planetmath.org/encyclopedia/TypesOfHomomorphisms.html
where these notions are defined from the point of view of Universal Algebra, not category theory.

Regular mono/epimorphisms are defined in
http://planetmath.org/encyclopedia/Equalizer.html

I'll add extremal mono/epimorphisms in a separate entry.

quetion: do it makes sense to speak of a <<homomorphism>> between open sets of complex vector spaces?

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