Comparison of functors

Selected: contravariant power set functor, covariant power set functor. Choose different functors.

Property	$P_{\forall}$	$P_{\exists}$
cocontinuous
cofinitary
comonadic
conservative
continuous
coreflector
coregular
dominant
equivalence
essentially injective
essentially surjective
exact
faithful
finitary
full
full on isomorphisms
fully faithful
isomorphism
left adjoint
left exact
left-invertible
monadic
preserves binary coproducts
preserves binary products
preserves coequalizers
preserves coproducts
preserves coreflexive equalizers
preserves epimorphisms
preserves equalizers
preserves finite coproducts
preserves finite products
preserves initial objects
preserves monomorphisms
preserves products
preserves reflexive coequalizers
preserves regular epimorphisms
preserves regular monomorphisms
preserves terminal objects
pseudomonic
reflector
regular
representable
right adjoint
right exact
right-invertible