Implication Details
Claim: If a functor is a right adjoint, then it is continuous.
Proof: This is standard, see Mac Lane, Ch. V, Theorem 5.1.
Show 25 functors using this implication
- abelianization functor for groups
- binary coproduct functor on sets
- binary diagonal functor on the category of sets
- contravariant power set functor
- countable copower functor on sets
- covariant power set functor
- discrete topology functor
- doubling functor on sets
- enveloping group functor
- forgetful functor from abelian groups to groups
- forgetful functor from groups to monoids
- forgetful functor from groups to pointed sets
- forgetful functor from rings to monoids
- free group functor
- fundamental group functor
- group of units functor
- indiscrete topology functor
- modulo p functor
- monoid ring functor
- opposite category functor
- opposite monoid functor
- p-torsion functor
- path components functor
- squaring functor on sets
- torsion functor