Implication details

Claim: If a category is pointed and has a subobject classifier, then it is 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.

This implication has a dual.

Show 6 categories using this implication