Logical functor
= Logical functor
A logical functor between elementary toposes preserves <finite limits>, <exponential objects> and the <subobject classifier>, with their canonical comparison maps. It therefore preserves <power objects> and the double-power-object monad. If it has a left adjoint, <power-object monadicity> and the <adjoint lifting theorem for monad algebra functors> give it a right adjoint as well.