I have a rather simple question though I couldn't find the answer here. Do monomorphisms (epimorphisms) have left (right) inverses in the category of abelian groups? How can we prove this fact knowing that the kernel (cokernel) must be trivial in this case? Will be also glad just for the link with the proof.
2026-03-30 16:59:04.1774889944
Monomorphisms and epimorphisms in Ab
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$f:\Bbb Z\to\Bbb Z$ given by $f(a)=2a$ has no left inverse.
The projection $\pi:\Bbb Z\to \Bbb Z/2\Bbb Z$ has no right inverse.