Implication details

Claim: Given a functor whose codomain is trivial, and whose domain has an initial object, then it is a coreflector.

Proof: Let

F : \C \to 1

be the unique functor into the trivial category, and assume that

\C

has an initial object

X

Then the constant functor

X : 1 \to \C

is fully faithful and left adjoint to

F

because

\Hom(X(*),Y) \cong * \cong \Hom(*,F(Y))

This implication has a dual.

Show 3 functors using this implication