A semantic framework for modeling the dynamics of object systems is proposed, based on algebraic methods and formulated categorically. The static properties of objects are described by algebraic specifications which could be given as the public interfaces of class specifications. Objects are persistent entities which survive method executions allowing the model to distinguish between object identity and object values. Configurations of objects are modeled by many-sorted algebras and each configuration represents a community of objects (possibly related) with a given state. Configurations can evolve through state changes modeled via non homomorphic algebra transformations. The configurations and the evolutions form a category which represents an object transition system. The structure of the object transition system may reflect the architecture of the interconnections of the software system components (classes).