Every non-trivial right adjoint functor between generalized quasi-varieties decomposes into a matrix power followed by a solution-set construction, and this decomposition is dual to a new notion of logical translation.
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A logical and algebraic characterization of adjunctions between generalized quasi-varieties
Every non-trivial right adjoint functor between generalized quasi-varieties decomposes into a matrix power followed by a solution-set construction, and this decomposition is dual to a new notion of logical translation.