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Homotopies in Grothendieck fibrations

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arxiv 1905.10690 v3 pith:YXLAC5CM submitted 2019-05-25 math.CT math.AT

Joseph Helfer This is my paper · ORCID
classification math.CTmath.AT
keywords mathbfcategorycategoriesconstructionfibrationfibrationsgrothendieckapplied
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abstract

We define a natural 2-categorical structure on the base category of a large class of Grothendieck fibrations. Given any model category $\mathbf{C}$, we apply this construction to a fibration whose fibers are the homotopy categories of the slice categories $\mathbf{C}/A$, and we show that in the case $\mathbf{C}=\mathbf{Top}$, our construction applied to this fibration recovers the usual 2-category of spaces.

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  1. First-order homotopical logic

    math.LO 2019-08 conditional novelty 6.0 of 10

    A homotopy-theoretic semantics for intuitionistic first-order logic is formulated with Grothendieck fibrations, and the paper proves homotopy invariance using 1-discrete 2-fibrations.

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