Partial pullback complement rewriting

A. R. Shir Ali Nasab, S. N. Hosseini

Abstract: In this article, we first characterize the existence of certain pullback complements in a category, in terms of the existence of exponentials in a corresponding slice category and also in terms of the existence of pullbacks in the corresponding partial morphism category. We also prove that certain pullback complements exist in a weak adhesive VK category if and only if they exist in the corresponding partial morphism category.We then propose a new graph rewriting technique, called the partial pullback complement rewriting, that uses pullback complements in a partial morphism category. We finally compare this with the double-pullback, single pushout, double-pushout and sesqui-pushout techniques, proving that in certain categories and under certain conditions, the partial pullback complement rewriting, implies and/or is implied by the above mentioned rewritings. Some illustrative examples are also given.