1 citations · 1 across the 8 of their papers we have counts for
8 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,…
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…
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 gr…
Cost-sensitive computational adequacy of higher-order recursion in synthetic domain theory
Yue Niu, Jonathan Sterling, Robert Harper
We study a cost-aware programming language for higher-order recursion dubbed in the setting of synthetic domain theory (SDT). Our main contribution rel…
Tensorial structure of the lifting doctrine in constructive domain theory
Jonathan Sterling
We present a survey of the two-dimensional and tensorial structure of the lifting doctrine in constructive domain theory, i.e. in the theory of directed-complete partial orders (dc…