The Choice of Standards for a Reporting Language

The problem of information exchange arises in many contexts, ranging from computer science to linguistics to financial accounting. One aspect of this problem is the choice of whether to use a single standard for all users of information or whether to use different languages for different audiences; this has been of particular interest in international accounting contexts. This paper creates a framework (specifically, a mathematical category) for studying this issue. Topological spaces are used to model how an agent's understanding of the world is translated into a local reporting language, and a certain class of continuous functions captures when a local reporting environment can be translated into a standardized language. In general, standardization comes at the cost of allowing less information to be transmitted. The category presented here provides a method for studying settings where agents are not aware of the same objects and also for settings where agents need their standards to be not only mutually agreeable but also acceptable to outside parties. Thus, unawareness and incomplete contracting have natural interpretations in the framework presented here