9 papers
Conceptual completeness for subgeometric logics
Ivan Di Liberti, Umberto Tarantino, Lingyuan Ye
We explore the notion of conceptual completeness for a fragment of geometric logic in the framework developed by the first and third author. Unlike its traditional interpretation a…
Duality theory for categorical theories
Lingyuan Ye
We have generalised the notion of categorical theory in model theory to the context of coherent theories. We prove a duality result between the full sub-2-category of pretopoi whic…
The Synthetic Sierpiński Cone
Fredrik Bakke, Jonathan Sterling, Mark Damuni Williams +1
In domains, categories, and toposes, the Sierpiński cone construction glues onto a space a universal closed point lying below all the other points. Although this is a lax colimit,…
Coexact completion of profinite Heyting algebras and uniform interpolation
Lingyuan Ye
This paper shows that the sheaf representation of finitely generated free Heyting algebras constructed by Ghilardi and Zawadowski can be factored as the profinite completion of Hey…
Craig Interpolation for Subgeometric Logics
Ivan Di Liberti, Lingyuan Ye
We show that a vast class of finitary fragments of geometric logic admit a form of Craig interpolation property. In doing so, we provide a new dictionary to import technology from…
TRIDENT: A Trimodal Cascade Generative Framework for Drug and RNA-Conditioned Cellular Morphology Synthesis
Rui Peng, Ziru Liu, Lingyuan Ye +3
Accurately modeling the relationship between perturbations, transcriptional responses, and phenotypic changes is essential for building an AI Virtual Cell (AIVC). However, existing…
Logic and Concepts in the 2-category of Topoi
Ivan Di Liberti, Lingyuan Ye
We use Kan injectivity to axiomatise concepts in the 2-category of topoi. We showcase the expressivity of this language through many examples, and we establish some aspects of the…
Domains and Classifying Topoi
Jonathan Sterling, Lingyuan Ye
We explore a new connection between synthetic domain theory and Grothendieck topoi related to the distributive lattice classifier. In particular, all the axioms of synthetic domain…
Stack Representation of Finitely Presented Heyting Pretoposes I
Lingyuan Ye
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, wh…