34 citations · 95 across the 15 of their papers we have counts for
16 papers
Epimorphisms and Acyclic Types in Univalent Foundations
Ulrik Buchholtz, Tom de Jong, Egbert Rijke
We characterize the epimorphisms in homotopy type theory (HoTT) as the fiberwise acyclic maps and develop a type-theoretic treatment of acyclic maps and types in the context of syn…
Delooping the sign homomorphism in univalent mathematics
Éléonore Mangel, Egbert Rijke
In univalent mathematics there are at least two equivalent ways to present the category of groups. Groups presented in their usual algebraic form are called abstract groups, and gr…
Central H-spaces and banded types
Ulrik Buchholtz, J. Daniel Christensen, Jarl G. Taxerås Flaten +1
We introduce and study central types, which are generalizations of Eilenberg-Mac Lane spaces. A type is central when it is equivalent to the component of the identity among its own…
Introduction to Homotopy Type Theory
Egbert Rijke
This is an introductory textbook to univalent mathematics and homotopy type theory, a mathematical foundation that takes advantage of the structural nature of mathematical definiti…
Algebraic Presentations of Type Dependency
Benedikt Ahrens, Jacopo Emmenegger, Paige Randall North +1
C-systems were defined by Cartmell as the algebraic structures that correspond exactly to generalised algebraic theories. B-systems were defined by Voevodsky in his quest to formul…
Characterizations of modalities and lex modalities
J. Daniel Christensen, Egbert Rijke
A reflective subuniverse in homotopy type theory is an internal version of the notion of a localization in topology or in the theory of -categories. Working in homotopy typ…