Although many GIS data models are available, a declarative, operational, well-defined, implementation-independent, and object-oriented language is lacking. Based on the theory of many sorted algebra, this work presents a family of geometric data models. Some geographical data models of urban information systems are illustrated using homomorphism. According to the results, the preferred characteristics of mixing declarative and operational statements, multiple representations, tight interdependency among objects, and integration of vector and raster based systems can be achieved through this mechanism.