Implication Details

Assumptions: pointed, subobject classifier

Conclusions: normal

Proof: The universal property of $\top : 0 \to \Omega$ precisely says that every monomorphism $A \to B$ is the kernel of a unique morphism $B \to \Omega$ , so it is normal.

Show 5 categories using this implication

category of finite groups
category of groups
category of countable groups
category of sets and relations
category of pointed sets