Categorical Bass-Serre Theory for Tree Quotients

Jiacheng Tang

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arXiv · 2606.16869

Categorical Bass-Serre Theory for Tree Quotients

Jiacheng Tang

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Abstract

We develop a categorical framework for Bass-Serre theory, which recovers parts of classical and profinite Bass-Serre theories for tree quotients. More precisely, we show that in what we call a Bass-Serre category, a group object acting on a graph satisfying some assumptions can be recovered as the fundamental group of the associated graph of groups acting on the standard graph. Examples of Bass-Serre categories include the category of sets, the category of profinite spaces, and any Grothendieck topos.

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Jiacheng Tang. 2026-06-15. Categorical Bass-Serre Theory for Tree Quotients. https://arxiv.org/abs/2606.16869

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