= Adjoint lifting theorem for monad algebra functors
For a functor between <Eilenberg-Moore categories> lying over a right adjoint on the base categories and compatible with the monad structures, an adjoint lifting theorem constructs a left adjoint when the required reflexive coequalizers of algebra presentations exist. Applied through <power-object monadicity>, this converts a left adjoint of a <logical functor> into a right adjoint of that logical functor. The coequalizer hypotheses are part of the theorem; commutation with the forgetful functors alone is insufficient.
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