Implication Details
Claim: If a functor is fully faithful and is a left adjoint, then it is comonadic and is left-invertible.
Proof: This follows from the dual implication.
This implication has a dual.
Show 13 functors using this implication
- binary coproduct functor on sets
- countable copower functor on sets
- discrete topology functor
- doubling functor on sets
- empty functor to the category of sets
- forgetful functor from finite sets to sets
- forgetful functor from finite abelian groups to abelian groups
- forgetful functor from finite groups to groups
- forgetful functor from groups to monoids
- forgetful functor from torsion abelian groups to abelian groups
- free group functor
- inclusion functor from extended natural numbers to ordinal numbers
- span endpoints inclusion