The development of an IT strategy and ensuring that it is the best possible one for business is a key problem many organizations face. This problem is that of linking business architecture to IT architecture in general and application architecture specifically. Without this linkage it is difficult to manage the changes needed by the business and maximize the benefits from the information technology (IT) investments. Linking the two domains requires defining the two architectures using a “common language.” While the application architecture domain has developed tools and processes to define and represent the architecture, the business architecture domain, however, lacks such processes and tools to be useful for linking of the two. The chapter addresses several questions dealing with the linking of the business and the application architectures. The author proposes to use category theory related constructs and notions to represent the business and information architecture and the linkages.