20 citations · 82 across the 18 of their papers we have counts for
8 papers · 1 filter
Identity Types in Algebraic Model Structures and Cubical Sets
Andrew Swan
We give a general technique for constructing a functorial choice of very good paths objects, which can be used to implement identity types in models of type theories in direct mann…
Separating Path and Identity Types in Presheaf Models of Univalent Type Theory
Andrew Swan
We give a collection of results regarding path types, identity types and univalent universes in certain models of type theory based on presheaves. The main result is that path type…
Lifschitz Realizability as a Topological Construction
Michael Rathjen, Andrew Swan
We develop a number of variants of Lifschitz realizability for CZF by building topological models internally in certain realizability models. We use this to show some interesting m…
On Dividing by Two in Constructive Mathematics
Andrew Swan
A classic result due to Bernstein states that in set theory with classical logic, but without the axiom of choice, for all sets and , if then a…
Every metric space is separable in function realizability
Andrej Bauer, Andrew Swan
We first show that in the function realizability topos every metric space is separable, and every object with decidable equality is countable. More generally, working with syntheti…
W-Types with Reductions and the Small Object Argument
Andrew Swan
We define a simple kind of higher inductive type generalising dependent -types, which we refer to as -types with reductions. Just as dependent -types can be characterised…
Lifting Problems in Grothendieck Fibrations
Andrew Swan
Many interesting classes of maps from homotopical algebra can be characterised as those maps with the right lifting property against certain sets of maps (such classes are sometime…
Dynkin isomorphism and Mermin--Wagner theorems for hyperbolic sigma models and recurrence of the two-dimensional vertex-reinforced jump process
Roland Bauerschmidt, Tyler Helmuth, Andrew Swan
We prove the vertex-reinforced jump process (VRJP) is recurrent in two dimensions for any translation invariant finite range initial rates. Our proof has two main ingredients. The…