Clans are 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.

翻译：族是广义代数理论的表示，其包含的信息多于通过加布里埃尔-乌尔默对偶与模型的局部有限可表现范畴相关联的有限极限范畴。为将这种额外信息纳入考虑而对加布里埃尔-乌尔默对偶进行推广，我们提出了一种在族与配备了某种弱因子分解系统的局部有限可表现范畴之间的对偶理论。