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Stack Representation of Finitely Presented Heyting Pretoposes I (2402.13099v1)
Published 20 Feb 2024 in math.LO and math.CT
Abstract: This is the first of a series of papers on stack representation of finitely presented Heyting pretoposes. In this paper, we provide the first step by constructing a (2, 1)-site, which can be thought of as the site of finite Kripke frames, such that the (2,1)-category of finitely presented Heyting pretoposes contravariantly embeds into the (2,1)- topos of stacks on this (2, 1)-site. This provides an entry point to use categorical and higher sheaf-theoretic tools to study the properties of certain classes of intuitionistic first-order theories.
- Locally presentable and accessible categories, volume 189. Cambridge University Press.
- Theorie de Topos et Cohomologie Etale des Schemas I, II, III, volume 269, 270, 305 of Lecture Notes in Mathematics. Springer.
- Breiner, S. (2013). Scheme representation for first-order logic. Phd thesis, Carnegie Mellon University. Available at arXiv:1402.2600.
- Caramello, O. (2018). Theories, Sites, Toposes: Relating and studying mathematical theories through topos-theoretic’bridges’. Oxford University Press.
- Caramello, O. (2019). Denseness conditions, morphisms and equivalences of toposes. arXiv preprint arXiv:1906.08737.
- Proper factorization systems in 2-categories. Journal of Pure and Applied Algebra, 179(1-2):65–86.
- Sheaves, games, and model completions: A categorical approach to nonclassical propositional logics, volume 14. Springer Science & Business Media.
- Haigh, J. (1980). Essential geometric morphisms between toposes over finite sets. Mathematical Proceedings of the Cambridge Philosophical Society, 87(1):21–24.
- Johnstone, P. T. (2002). Sketches of an Elephant: A Topos Theory Compendium, volume 1, 2. Oxford University Press.
- An extension of the Galois theory of Grothendieck, volume 309. American Mathematical Soc.
- Sheaves in geometry and logic: A first introduction to topos theory. Springer Science & Business Media.
- Makkai, M. (1982). Stone duality for first order logic. In Studies in Logic and the Foundations of Mathematics, volume 107, pages 217–232. Elsevier.
- Makkai, M. (1993). The fibrational formulation of intuitionistic predicate logic i: completeness according to gödel, kripke, and läuchli. i. Notre Dame Journal of Formal Logic, 34(3):334–377.
- Moerdijk, I. (1985). An elementary proof of the descent theorem for grothendieck toposes. Journal of Pure and Applied Algebra, 37:185–191.
- nLab authors (2024). (n,r)-category. https://ncatlab.org/nlab/show/%28n%2Cr%29-category. Revision 59.
- Pitts, A. (1983a). Amalgamation and interpolation in the category of heyting algebras. Journal of Pure and Applied Algebra, 29(2):155–165.
- Pitts, A. M. (1983b). An application of open maps to categorical logic. Journal of pure and applied algebra, 29(3):313–326.
- Pitts, A. M. (1992). On an interpretation of second order quantification in first order intuitionistic propositional logic. The Journal of Symbolic Logic, 57(1):33–52.
- Rogers, M. (2023). Toposes of Topological Monoid Actions. Compositionality, 5.
- Shulman, M. (2024). Heyting 2-category. https://ncatlab.org/nlab/show/Heyting+2-category. Revision 1.
- Street, R. (1974). Fibrations and yoneda’s lemma in a 2-category. In Kelly, G. M., editor, Category Seminar, pages 104–133, Berlin, Heidelberg. Springer Berlin Heidelberg.
- Street, R. (1982). Two-dimensional sheaf theory. Journal of Pure and Applied Algebra, 23(3):251–270.
- Tendas, G. (2022). On continuity of accessible functors. Applied Categorical Structures, 30(5):937–946.
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