Categories of Games and their Fraïssé Theory
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908654218772480 |
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| author | Duzi, Matheus Szeptycki, Paul Tholen, Walter |
| author_facet | Duzi, Matheus Szeptycki, Paul Tholen, Walter |
| contents | Relying on recent generalizations of the Fraïssé theory to a broader category-theoretic context, we study the class of abstract finite games played between two players and show the existence of an infinitetly countable game which is ultrahomogeneous and universal with respect to said class. Certain peculiarities of our game categories which clash with the usual framework found in the literature then lead us to formulate weaker category-theoretic properties which still yield a universal and ultrahomogeneous Fraïssé limit, thus further generalizing the categorical framework for a Fraïssé theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Categories of Games and their Fraïssé Theory Duzi, Matheus Szeptycki, Paul Tholen, Walter General Mathematics Primary: 91A44, 18A05, Secondary: 18A35, 37B05 Relying on recent generalizations of the Fraïssé theory to a broader category-theoretic context, we study the class of abstract finite games played between two players and show the existence of an infinitetly countable game which is ultrahomogeneous and universal with respect to said class. Certain peculiarities of our game categories which clash with the usual framework found in the literature then lead us to formulate weaker category-theoretic properties which still yield a universal and ultrahomogeneous Fraïssé limit, thus further generalizing the categorical framework for a Fraïssé theory. |
| title | Categories of Games and their Fraïssé Theory |
| topic | General Mathematics Primary: 91A44, 18A05, Secondary: 18A35, 37B05 |
| url | https://arxiv.org/abs/2511.11642 |