Geodesic
A categorical characterization of a~~~${\scriptsize1}\!\!\!\!\bigcirc$-iteratively defined state of common knowledge
Contributions to game theory and management, Tome 14 (2021), pp. 329-341

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We present here a novel approach to the analysis of common knowledge based on category theory. In particular, we model the global epistemic state for a given set of agents through a hierarchy of beliefs represented by a presheaf construction. Then, by employing the properties of a categorical monad, we prove the existence of a state, obtained in an iterative fashion, in which all agents acquire common knowledge of some underlying statement. In order to guarantee the existence of a fixed point under certain suitable conditions, we make use of the properties entailed by Sergeyev's numeral system called grossone, which allows a finer control on the relevant structure of the infinitely nested epistemic states.
Keywords: common knowledge, category theory, grossone. 
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     title = {A categorical characterization of a~~~${\scriptsize1}\!\!\!\!\bigcirc$-iteratively defined state of common knowledge},
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     pages = {329--341},
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Fernando Tohmé; Gianluca Caterina; Rocco Gangle. A categorical characterization of a~~~${\scriptsize1}\!\!\!\!\bigcirc$-iteratively defined state of common knowledge. Contributions to game theory and management, Tome 14 (2021), pp. 329-341. http://geodesic.mathdoc.fr/item/CGTM_2021_14_a24/