Object Inheritance Beyond Subtyping

. A categorial semantic domain for objects is presented in order to clarify both aggregation and specialization. Three kinds of specialization are discussed: (1) subtyping (specialization with no side effects and no nonmonotonic overriding); (2) monotonic specialization (possibly with side effects but still only with monotonic overriding); and (3) non-monotonic specialization (possibily with side effects and non-monotonic overriding). A sequence of three categories of objects differing only in the morphisms is presented. The first one is used to explain object aggregation (respecting locality through a frame constraint) and the strictest form of specialization (subtyping). The second category is shown to be adequate for explaining specialization with side effects (by relaxing the frame constraint). Finally, the third category supports also nonmonotonic overriding, by adopting as morphisms suitable partial morphisms of the second one. All these categories are complete and cocomplete. Co..