Implication Details
Claim: Given a functor whose domain has reflexive coequalizers, if it is conservative and preserves preserves reflexive coequalizers and is a right adjoint, then it is monadic.
Proof: This is the crude monadicity theorem. A proof can be found in Mac Lane & Moerdijk, Thm. IV.4.2.
Show 9 functors using this implication
- binary diagonal functor on the category of sets
- contravariant power set 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
- indiscrete topology functor
- squaring functor on sets
- trivial functor from the delooping