Implication details
Claim: Given a functor whose domain has coproducts and is locally essentially small, if it is representable, then it is a right adjoint.
Proof: If is a locally small category with coproducts and is any object, then the copower functor , is left adjoint to .
Show 10 functors using this implication
- binary product functor on sets
- forgetful functor for groups
- forgetful functor for rings
- forgetful functor for topological spaces
- forgetful functor for vector spaces
- identity functor on the category of sets
- ring idempotents functor
- sequences functor on sets
- simple-group probing functor
- walking morphism representation