To reuse previous knowledge of object-oriented design and adapt them to solve new problems, the collaboration relationships and the responsibility distribution among software objects need to be thoroughly understood and precisely formulated. The paper proposes a knowledge-based approach that employs category theoretic models to formalize and mechanize object-oriented software design and synthesis by focusing concern on reasoning about the interdependency relationships at different levels of abstraction and granularity. The major benefit of our approach is twofold: First, it provides an explicit semantics for formal object-oriented specifications, and therefore enables a high-level of reusability and dynamic adaptability. Second, it utilizes the ability of categorical computations to support automated software composition and refinement. A prototype tool that demonstrates the feasibility and effective of our approach is also presented.