2026-09-22T20:51:36Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/116237 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Rezk, Charles Stojanoska, Vesna Ando, Matthew Heller, Jeremiah 2022-08 application/pdf en text Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms The student, Robert Rennie, accepted the attached license on 2022-07-14 at 00:28. The student, Robert Rennie, submitted this Dissertation for approval on 2022-07-14 at 01:01. This Dissertation was approved for publication on 2022-07-14 at 15:09. DSpace SAF Submission Ingestion Package generated from Vireo submission #18296 on 2022-11-15 at 18:21:00 Quasicategorical Galois theories Rennie, Robert Joseph 2022-07-14 quasicategorical Galois theorem higher category theory Galois theory duality quasicategory enhanced mapping space Segal groupoid Segal groupoid object internal presheaves splitting object splitting algebra The classification of 1-toposes given by [Joyal-Tierney '84] admits a proof with a `categorical Galois theorem' playing a central role, as discussed in Galois Theories by Francis Borceux.. Our main result, Theorem 2.4.3, refines this result to a `quasicategorical Galois theorem.' Before we state and prove our main result, we expand upon the Mathematical content, and applicability, of the 1-categorical analogue. Specifically, we show how to begin with a duality result, and produce an application of the 1-categorical Galois theorem which mirrors the classical Galois theory of fields, rings, and covering spaces. We also offer a broadly accessible motivation for the 1-categorical Galois theorem, and hence for our quasicategorical Galois theorem. Finally, the proof of our main result is written as explicitly as possible toward the eventual goal of a model-independent generalization. Thesis eng https://hdl.handle.net/2142/116237 Copyright 2022 Robert Rennie Ph.D. Dissertation Mathematics University of Illinois at Urbana-Champaign Mathematics