Early Geospatial Information Systems (GIS) dealt with static objects. There is much demand, however, to include temporal objects in these systems. Many have studied this problem and suggested technical solutions for different spatial operations. A common shortcoming is that the extension techniques are highly dependent on the specific case studies and cannot be generalized. In this paper, we propose studying spatial operations via their dimension-independent properties. This research intends to construct a mathematical framework that contains primitives for different operations. The framework will be independent of the space in which the operations are applied using algebraic structures-and more specifically category theory-that ignore those properties of operations which depend on the objects they are applied to. Implementations for some case studies are presented.