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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2511.21623 |
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| _version_ | 1866918218960994304 |
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| author | Abdou, Joseph |
| author_facet | Abdou, Joseph |
| contents | 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 political sites consists of a pair of maps, namely a Base map and a Ground map, satisfying appropriate conditions. Two functors relate the Foundation and the Configuration: the Knit which attributes to each p-site a p-formation and the Nerve which attributes to each p-site a simplicial complex. In the opposite direction a functor, called Canon, which attributes to any p-formation its canonical p-site, turns out to be in an appropriate sense the inverse of the Knit and the Nerve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21623 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Category of the Political \Large{Part I - Homónoia} Abdou, Joseph Category Theory 18 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 political sites consists of a pair of maps, namely a Base map and a Ground map, satisfying appropriate conditions. Two functors relate the Foundation and the Configuration: the Knit which attributes to each p-site a p-formation and the Nerve which attributes to each p-site a simplicial complex. In the opposite direction a functor, called Canon, which attributes to any p-formation its canonical p-site, turns out to be in an appropriate sense the inverse of the Knit and the Nerve. |
| title | A Category of the Political \Large{Part I - Homónoia} |
| topic | Category Theory 18 |
| url | https://arxiv.org/abs/2511.21623 |