Implication Details
Claim: If a functor is representable, then it is continuous.
Proof: This is standard, see Mac Lane, Ch. V, Theorem 4.1.
Show 12 functors using this implication
- binary coproduct functor on sets
- binary product functor on sets
- countable copower functor on sets
- covariant power set functor
- doubling 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
- path components functor
- sequences functor on sets