Clans are representations of generalized algebraic theories that contain more information than the finite-limit categories associated to the l.f.p. categories of models via Gabriel-Ulmer duality. Refining Gabriel-Ulmer duality to account for this additional information, this article presents a duality theory between clans and l.f.p. categories equipped with a weak factorization system subject to axioms.

翻译：宗族是对广义代数理论的表示，其包含的信息多于通过加布里埃尔-乌尔默对偶性与模型局部有限展现范畴相关联的有限极限范畴。本文通过精炼加布里埃尔-乌尔默对偶性以解释这些额外信息，提出了一种在宗族与配备有满足公理条件的弱因子分解系统的局部有限展现范畴之间的对偶理论。