Epimorphisms and Acyclic Types in Univalent Foundations
Logic in Computer Science
2025-02-12 v3 Algebraic Topology
Category Theory
Abstract
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 synthetic homotopy theory as developed in univalent foundations. We present examples and applications in group theory, such as the acyclicity of the Higman group, through the identification of groups with 0-connected, pointed 1-types. Many of our results are formalized as part of the agda-unimath library.
Cite
@article{arxiv.2401.14106,
title = {Epimorphisms and Acyclic Types in Univalent Foundations},
author = {Ulrik Buchholtz and Tom de Jong and Egbert Rijke},
journal= {arXiv preprint arXiv:2401.14106},
year = {2025}
}
Comments
To appear in The Journal of Symbolic Logic