Descent Constraints in Higher Topos Theory and the Construction of Univalent Universes
Year: 2025
Type: article
Abstract: Mathematical Applications of Science Fiction We present a rigorous construction of univa-lent universes within the framework of arbitraryGrothendieck (∞, 1)-topoi, subject to transfinite de-scent constraints. By generalizing the descent dataof simplicial presheaves to a hyper-complete setting,we formulate a coherence theorem for the modulistack of object classifiers. We introduce the notionof a transfinite Reedy fibration over the ordinal filtra-tion of the site, proving that the univalence axiomarises naturally as a descent condition for the repre-sentable functor of the universe object. We furtherdemonstrate that for any κ-compact ∞-topos T, theobject classifier Uκ satisfies the effective descent prop-erty with respect to the canonical topology, providedthe underlying model category admits a transfinitesequence of Quillen adjunctions stabilizing at κ.
Authors: Revista, Zen, MFC, 10
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7117872355
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