English

Formalizing the zigzag construction of path spaces of pushouts

Logic 2025-10-10 v1 Algebraic Topology

Abstract

A recent pre-print of W\"arn gives a novel pen-and-paper construction of a type family characterizing the path spaces of an arbitrary pushout, and a natural language argument for its correctness. We present the first formalization of the construction and a proof that it is fiberwise equivalent to the path spaces. The formalization is carried out in axiomatic homotopy type theory, using the Agda proof assistant and the agda-unimath library.

Keywords

Cite

@article{arxiv.2510.08452,
  title  = {Formalizing the zigzag construction of path spaces of pushouts},
  author = {Vojtěch Štěpančík},
  journal= {arXiv preprint arXiv:2510.08452},
  year   = {2025}
}

Comments

15 pages, 4 figures, submitted to CPP 2026