By preadditive category I mean Ab-enriched with zero object.
As I understand, zero morphisms are the ones factored through zero objects and zero elements are the identity of the group structure on the enrichment on Homs.
It's clear that if the identity is a zero morphism, then the object is zero: $$x = x\circ id = x\circ0 = 0$$ but does this also happen if the identity is a zero element? why?
Is there any relationship between the zero morphism and the zero element?
Thanks in advance.