Mathematics > Logic
arXiv:2606.01165 (math)
[Submitted on 31 May 2026]
Abstract:Ramesh's 2023 dissertation introduces the categorical notions of introspective theories and geminal categories, which formalize "self-internalizing" structures sharing the form of Löb's theorem ($\Box A \vdash A$ implies $\vdash A$). We reorganize the theory of geminal categories in a self-contained manner by introducing "code structures on fibrations," which serve as a categorical abstraction of Gödel coding. This framework leads to a significant simplification of the proof of Löb's theorem for geminal categories, as well as to a new categorical counterpart of the Gödel-Löb axiom ($\Box(\Box A \to A) \to \Box A$). This formulation offers an accessible framework for Ramesh's approach and suggests connections to modal type theories, where similar meta- and object-level interactions arise.
| Comments: | 80 pages. Master's thesis, the University of Tokyo |
| Subjects: | Logic (math.LO); Logic in Computer Science (cs.LO); Category Theory (math.CT) |
| MSC classes: | 03G30 (Primary) 03F40, 03F45, 18D30, 18D40, 18C10 (Secondary) |
| ACM classes: | F.4.1 |
| Cite as: | arXiv:2606.01165 [math.LO] |
| (or arXiv:2606.01165v1 [math.LO] for this version) | |
| https://doi.org/10.48550/arXiv.2606.01165 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Yuto Ikeda [view email]
[v1]
Sun, 31 May 2026 11:14:17 UTC (2,014 KB)
Current browse context:
math.LO
Bookmark
Bibliographic Tools
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Code, Data, Media
Code, Data and Media Associated with this Article
Demos
Demos
Related Papers
Recommenders and Search Tools
About arXivLabs
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.