A variety of restricted functor categories has been investigated independently and for different purposes to provide double-pushout-rewriting in the areas of model-driven development and graph transformation. We introduce S-cartesian functor categories as a unifying formal framework for these different examples. S-cartesian functor categories are certain subcategories of functor categories that preserve the adhesiveness of their base categories. We show the comprehensive theory of double-pushout-rewriting for S-cartesian functor categories which fulfill additional sufficient conditions. As a new application, we introduce the categories PTrG and APTrG of partial triple graphs and attributed partial triple graphs as S-cartesian functor categories and obtain all the classical results for double-pushout-rewriting in these categories by construction. Partial triple graphs have recently been used to improve model synchronization processes.

已对各种受限函子类别进行了独立研究，并针对不同目的在模型驱动的开发和图形转换领域中提供了双重推送重写。我们介绍了S-笛卡尔函子类别，作为这些不同示例的统一正式框架。S-笛卡尔函子类别是函子类别的某些子类别，可保留其基本类别的粘合性。我们展示了满足其他充分条件的S-笛卡尔函子类别的双推重写的综合理论。作为一个新的应用程序，我们引入类别PTRG和APTrG的部分三倍图形和将部分三元图归为S-笛卡尔函子类别，并通过构造获得这些类别中的双重推出重写的所有经典结果。最近已使用部分三元图来改进模型同步过程。