Research
My research interests are in mathematical logic, topology, type theory and their interaction with category theory. Most of my recent efforts are devoted to give a definition of logic (), and to study fragments of geometric logic (). I also do many other things in the broad topic of general and formal category theory, categorical logic, (infinity-)topos theory, and semantics of dependent type theory.
7. Conceptual completeness for subgeometric logics.
July 2026. j/w Umberto Tarantino and Lingyuan Ye. New.
6. Polarities, voltages, and capacitors: a categorical approach to hulls, envelopes, and completions.
March 2026. j/w Martino Lupini. Submitted to Journal of Pure and Applied Algebra.
5. Craig interpolation for subgeometric logics.
Jan 2026. j/w Lingyuan Ye. Submitted to Journal of Symbolic Logic in Jan 2026.
4. Classifying ∞-topoi via weighted limits.
Dec 2025. j/w Nicholas J. Meadows. Submitted to Journal of the London Mathematical Society in Jan 2026.
3. Logics and concepts in the 2-category of Topoi.
Apr 2025. j/w Lingyuan Ye. Submitted to Annals of Pure and Applied Logic in Spring 2025.
Mar 2024. j/w Morgan Rogers. Under revision.
1. Sketches and Classifying Logoi.
Mar 2024. j/w Gabriele Lobbia. Submitted to Advances in Mathematics in Spring 2024.
17. Bi-accessible and bipresentable 2-categories.
Applied Categorical Structures. Oct 2024. j/w Axel Osmond.
16. Adjoint functor theorems for lax-idempotent pseudomonads.
Theory and Applications of Categories. May 2024. j/w Nathanael Arkor, Fosco Loregian.
15. Context, Judgement, Deduction.
Accepted by Proceedings of CatMi 2023. May 2024. j/w Greta Coraglia.
14. Coalgebras for Vietoris and monadicity.
The Journal of Symbolic Logic. Feb 2024. j/w Marco Abbadini.
13. The geometry of coherent topoi and Ultrastructures.
Conditionally accepted by The Journal of Symbolic Logic. Feb 2024.
12. Formal Model Theory & Higher Topology.
Mathematical Logic Quarterly. Nov 2023.
11. KZ-pseudomonads and Kan Injectivity.
Theory and Applications of Categories. July 2023. j/w Gabriele Lobbia, Lurdes Sousa.
10. Accessibility and presentability in 2-categories.
Journal of Pure and Applied Algebra May 2022. j/w Fosco Loregian.
9. Exponentiable Grothendieck categories in flat Algebraic Geometry.
Journal of Algebra. Mar 2022. j/w Julia Ramos González.
8. Enriched locally generated categories.
Theory and Applications of Categories. Mar 2022. j/w Jiří Rosický.
7. General facts on the Scott Adjunction.
Applied Categorical Structures. Sept 2021.
Journal of Pure and Applied Algebra. May 2021.
5. Functorial semantics for partial theories.
ACM Principles of Programming Languages 2021 (POPL21). Oct 2020. j/w Fosco Loregian, Chad Nester, Pawel Sobocinski.
4.Gabriel-Ulmer duality for topoi and its relation with site presentations.
Applied Categorical Structures. Aug 2020. j/w Julia Ramos González.
3. Codensity: Isbell duality, pro-objects, compactness and accessibility.
Journal of Pure and Applied Algebra. Apr 2020.
2. Weak saturation and weak amalgamation property.
The Journal of Symbolic Logic. Jul 2019.
1. Homotopical Algebra is not concrete.
Journal of Homotopy and Related Structures. Feb 2018. j/w Fosco Loregian.
1. On the unicity of formal category theories.
Jan 2019. j/w Fosco Loregian. Never finished. The community seem to have now digested the intended wisdom of the paper.
Sept 2020. Doctoral dissertation.
Preprints
Publications
Notes with no intention of publication
Ph.D thesis