2019/08/23 by Joseph Helfer, Helfer, Joseph
Computer Science · #18C50 (Primary) 18D30 #55U35 (Secondary) #Advanced Algebra and Logic #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · doi:10.48550/arxiv.1908.08944
openalex publication_date 2019/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a homotopy-theoretic interpretation of intuitionistic first-order logic based on ideas from Homotopy Type Theory. We provide a categorical formulation of this interpretation using the framework of Grothendieck fibrations. We then use this formulation to prove the central property of this interpretation, namely homotopy invariance. To do this, we use the result from arXiv:1905.10690 that any Grothendieck fibration of the kind being considered can automatically be upgraded to a 2-dimensional fibration, after which the invariance property is reduced to an abstract theorem concerning pseudonatural transformations of morphisms into 2-dimensional fibrations.