Implication Details
Claim: Given a functor whose domain has coreflexive equalizers, if it is conservative and is a left adjoint and preserves preserves coreflexive equalizers, then it is comonadic.
Proof: This follows from the dual implication.
Claim: Given a functor whose domain has coreflexive equalizers, if it is conservative and is a left adjoint and preserves preserves coreflexive equalizers, then it is comonadic.
Proof: This follows from the dual implication.