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arXiv · 2510.08452

Formalization of the zigzag construction of path spaces of pushouts in homotopy type theory

Vojtěch Štěpančík
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Abstract

A pre-print of W\"arn gives a pen-and-paper construction of a type family characterizing the path spaces of an arbitrary pushout, and a natural language argument for its correctness. This paper presents 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.

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Vojtěch Štěpančík. 2025-10-09. Formalization of the zigzag construction of path spaces of pushouts in homotopy type theory. https://arxiv.org/abs/2510.08452

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