8 papers
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…
The Synthetic SierpiÅski Cone
Fredrik Bakke, Jonathan Sterling, Mark Damuni Williams +1
In domains, categories, and toposes, the SierpiÅski cone construction glues onto a space a universal closed point lying below all the other points. Although this is a lax colimit,…
Reflexive graph lenses in univalent foundations
Jonathan Sterling
Martin-Löf's identity types provide a generic (albeit opaque) notion of identification or "equality" between any two elements of the same type, embodied in a canonical reflexive g…
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…
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…
When is the partial map classifier a SierpiÅski cone?
Leoni Pugh, Jonathan Sterling
We study the relationship between partial map classifiers, SierpiÅski cones, and axioms for synthetic higher categories and domains within univalent foundations. In particular, we…