On the Nielsen-Schreier Theorem in Homotopy Type Theory

Andrew W Swan

doi:10.46298/lmcs-18(1:18)2022

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arXiv · 2010.01187

On the Nielsen-Schreier Theorem in Homotopy Type Theory

Andrew W Swan

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Abstract

We give a formulation of the Nielsen-Schreier theorem (subgroups of free groups are free) in homotopy type theory using the presentation of groups as pointed connected 1-truncated types. We show the special case of finite index subgroups holds constructively and the full theorem follows from the axiom of choice. We give an example of a boolean infinity topos where our formulation of the theorem does not hold and show a stronger "untruncated" version of the theorem is provably false in homotopy type theory.

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BibTeX RIS

Andrew W Swan. 2020-10-02. On the Nielsen-Schreier Theorem in Homotopy Type Theory. https://doi.org/10.46298/lmcs-18(1%3A18)2022

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