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arXiv · 2609.32816

The third symmetric product of a set is a set in HoTT

Wojciech Paupa
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Abstract

We deformalize an LLM-generated proof within the formalism of Homotopy Type Theory that an iterated pushout construction for $\operatorname{SP}^3(X)$ is a set whenever $X$ is a set. The proof expands on a similar proof by Buchholtz for $\operatorname{SP}^2(X)$, employing a similar encode-decode strategy and the same formal machinery.

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Wojciech Paupa. 2026-09-26. The third symmetric product of a set is a set in HoTT. https://arxiv.org/abs/2609.32816

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