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Many organizations perceive the importance of linking business architecture to application architecture. It is difficult to manage the changes needed by the business and maximize the benefits from the information technology (IT) investments without this linkage. Linking the two domains require that we define the two architectures using a "common language". The architecture domain has tools and processes to define and represent the architecture, and use it to build the related processes and services. The business architecture domain, however, lacks any and/or are not matured enough to be useful for linking of the two. We address questions dealing with the linking of the business and the information/application architectures. Specifically, how do we define business architecture useful for linking? How do we represent these architectures and what "language" should we use? We propose the use Category theory related constructs and notions to represent both the business and information architecture. The work reported here is primarily the current status of research in the area of business architecture, application architecture and linking these two.