Every split monomorphism is a monomorphism.
When is the converse true in vector spaces?

Question

Every split monomorphism is a monomorphism.
When is the converse true in vector spaces?

anonymous · Answer

what class is this? discrete math , linear algebra??

anonymous · Answer

Its an abstract algebra class subject( category theory). I know that in sets the converse will not be true when you have a map from the empty set to a non-empty set. I am confused about what happens in vector spaces. Any Ideas?

anonymous · Answer

it has been a while, but i think in the category "vector space" all exact sequences split

anonymous · Answer

in other words the converse is always true for vector spaces.

anonymous · Answer

i also remember reading this sometime last year. let me see if i can find it

anonymous · Answer

try here http://unapologetic.wordpress.com/2008/06/26/exact-sequences-split/

anonymous · Answer

Thank you I will have a look at that.