The Exact Completion of the Category of Polish Groups

Martino Lupini

arXiv:2608.13693v1 Primary: math.CT Secondary: math.GN, math.GR, math.KT, math.LO

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.

Disclosure

“fts and its locally compact and Lie consequences. Acknowledgments. The author is grateful to Ronnie Chen and Ivan Di Liberti for many useful conversations and to the Association of Neurodivergent Logicians (NeuroLogic) for its support. ChatGPT by OpenAI (version GPT-5.6 Sol) was used in the preparation of this manuscript.”
PDF page 3

Classification: Drafting limited passages
Multiplier: 5
Verified: 2026-08-23T05:14:31.460979Z

Structural counts

Pages 34 pdf

Theorems 5 source

Lemmas 5 source

Propositions 7 source

Corollaries 5 source

Definitions 8 source

Displayed equations 74 source

Bibliography entries 6496 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file polish-group-exact-completion-and-approximately-multiplicative-lifts-2026-08-13-tris.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.