The Exact Completion of the Category of Polish Groups

Martino Lupini

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arXiv · 2608.13693

The Exact Completion of the Category of Polish Groups

Martino Lupini

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Abstract

This article shows that the exact completion as a regular category of the homological category of Polish groups and continuous group homomorphisms is the category of groups with a Polish cover and Borel-definable group homomorphisms. We also obtain several equivalent characterizations for the morphisms in the exact completion. An analogous description is deduced for several important subcategories of the category of Polish groups.

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Martino Lupini. 2026-08-13. The Exact Completion of the Category of Polish Groups. https://arxiv.org/abs/2608.13693

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