Synthetic perspectives on spaces and categories
Category Theory
2025-10-20 v1 Algebraic Topology
Logic
Abstract
Recently discovered domain-specific formal systems -- specifically homotopy type theory and simplicial type theory -- provide new perspectives on spaces and categories in a natively equivalence-invariant setting. In this note, we expose fundamental proof techniques from these parallel settings: describing induction principles over paths or arrows and constructions involving universes that are either univalent or directed univalent.
Cite
@article{arxiv.2510.15795,
title = {Synthetic perspectives on spaces and categories},
author = {Emily Riehl},
journal= {arXiv preprint arXiv:2510.15795},
year = {2025}
}
Comments
to appear in the International Congress of Mathematicians Proceedings 2026