A Monad-Based Formalization of Common Knowledge

We present here a novel approach to the analysis of common knowledge based on Category Theory. We formalize knowledge hierarchies as presheaves over a category of agent sequences. The category of these presheaves constitutes a topos. We define an unfolding monad on the resulting topos, and use a Knaster–Tarski theorem to obtain common knowledge as a greatest fixed point under natural uniformity and exchangeability conditions on agent sequences.