DUALITY FOR CLANS: AN EXTENSION OF GABRIEL–ULMER DUALITY

Abstract Clans are categorical representations of generalized algebraic theories that contain more information than the finite-limit categories associated to the locally finitely presentable categories of models via Gabriel–Ulmer duality. Extending Gabriel–Ulmer duality to account for this additional information, we present a duality theory between clans and locally finitely presentable categories equipped with a weak factorization system of a certain kind.