A Category of the Political \Large{Part I - Hom\'onoia}
Joseph Abdou

TL;DR
This paper develops a mathematical framework using category theory to model political organizations and their transformations, introducing new categorical structures like p-formation and p-site to represent polity configurations.
Contribution
It introduces a novel categorical model of political structures, defining new constructs such as p-formation and p-site, and establishes functors relating these structures.
Findings
Defines categories for political configuration and foundation
Establishes functors Knit, Nerve, and Canon linking these categories
Provides a formal mathematical description of polity transformations
Abstract
This research aims at providing a mathematical model of the organization of the polity and its transformation. For that purpose we construct two categories named respectively Political Configuration and Political Foundation. Our construction depends on a couple of variables called the foundational pair. One variable, called the Base, consists of a finite number of members (agents), while the other, called the Ground, consists of a set of states that reflect all relevant interests/values/aspirations of the base members. An object of the Configuration, called p-formation, extends the notion of simplicial complex, and a morphism, which expresses the recomposition of the base, extends the notion of simplicial map. An object of the Foundation, called p-site, describes the profile of the polity, that is, how the states of the ground are intertwined between the agents. A morphism between…
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Taxonomy
TopicsPolitical Theory and Democracy · Sociology, Governance, and Technology · Populism, Right-Wing Movements
