A Category for Studying the Standardization of Reporting Languages

The problem of information exchange among agents who see the world subjectively arises in many contexts. One aspect of this problem is the choice of whether to use a standardized terminology among all agents or to use different languages for different audiences; this has been of particular interest in international accounting contexts. We develop a formal structure for studying this issue. An agent's reporting environment is modeled as a topological space, where the open neighborhoods represent ways that the agent can report (approximately) what he wishes to convey. We then develop a category of reporting environments, called Rep, and model the translation of one reporting environment to another as a homomorphism in this category. We show that reporting in a standardized language is different from using information in that language; this is because homomorphisms may only exist in one direction. Potential future applications are studying settings where agents are not aware of the same things (modeled as pullbacks) or where reports concern parties in addition to the reporting entity and the end user (modeled as pushouts)