13 citations · 17 across the 3 of their papers we have counts for
6 papers
Univalent foundations and the equivalence principle
Benedikt Ahrens, Paige Randall North
In this paper, we explore the 'equivalence principle' (EP): roughly, statements about mathematical objects should be invariant under an appropriate notion of equivalence for the ki…
A Higher Structure Identity Principle
Benedikt Ahrens, Paige Randall North, Michael Shulman +1
The ordinary Structure Identity Principle states that any property of set-level structures (e.g., posets, groups, rings, fields) definable in Univalent Foundations is invariant und…
A Hurewicz Model Structure for Directed Topology
Sanjeevi Krishnan, Paige Randall North
This paper constructs an h-model structure for diagrams of streams, locally preordered spaces. Along the way, the paper extends some classical characterizations of Hurewicz fibrati…
Type-theoretic weak factorization systems
Paige Randall North
This article presents three characterizations of the weak factorization systems on finitely complete categories that interpret intensional dependent type theory with Sigma-, Pi-, a…
Identity types and weak factorization systems in Cauchy complete categories
Paige Randall North
It has been known that categorical interpretations of dependent type theory with Sigma- and Id-types induce weak factorization systems. When one has a weak factorization system (L,…
Towards a directed homotopy type theory
Paige Randall North
In this paper, we present a directed homotopy type theory for reasoning synthetically about (higher) categories, directed homotopy theory, and its applications to concurrency. We s…