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When is the partial map classifier a Sierpiński cone?
Leoni Pugh, Jonathan Sterling
We study the relationship between partial map classifiers, Sierpiński cones, and axioms for synthetic higher categories and domains within univalent foundations. In particular, we…
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…
Hofmann-Streicher lifting of fibred categories
Andrew Slattery, Jonathan Sterling
In 1997, Hofmann and Streicher introduced an explicit construction to lift a Grothendieck universe from the category of sets into the category of set-valued presheaves on a small c…
Vietoris-Rips complexes of torus grids
Henry Adams, Adenike Yeside Adetowubo, Hector Barriga-Acosta +2
We study the topology of Vietoris--Rips complexes of finite grids on the torus. Let be the grid of points on the flat torus , equipped with the…