4 papers
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,…
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…