Model transformation is touted to play a key role in model-driven development. The mapping relations between models are the foundation and basis for the transformation. On the basis of software architecture, this paper tries to provide a precise semantics for both components structuring and models mapping by using category theory. Morphism composition is used to trace the interconnections and mapping relations between component-based models, while consistency between the sorts / operations of component models at different abstract levels is maintained by functors. Category theory supports the diagrammatic representation of component model that visualizes the relationships between components and the structural features, which can be used to strengthen the understandability and traceability of model transformation. The formalization enables users to check whether the mapping relations satisfy some desired properties and also is suitable to automatic software development, and thus can make an effective support to model-driven software development.