3 papers
math.AT2025
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…
math.CT2025
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…
cs.LO2024
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…