2023/08/22 by Dorette Pronk, Geoff Vooys, Pronk, Dorette +1
Mathematics · #14A99 #53C10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 18F40 #Secondary 18F20
paper · pdf · doi:10.48550/arxiv.2308.11753
openalex publication_date 2023/08/22 · openalex created_date 2023/08/25 · openalex updated_date 2026/08/03
In this paper we show that if \mathscrC is a category and if F\colon\mathscrCop → \mathfrakCat is a pseudofunctor such that for each object X of \mathscrC the category F(X) is a tangent category and for each morphism f of \mathscrC the functor F(f) is part of a strong tangent morphism (F(f),fα) and that furthermore the natural transformations fα vary pseudonaturally in \mathscrCop, then there is a tangent structure on the pseudolimit PC(F) which is induced by the tangent structures on the categories F(X) together with how they vary through the functors F(f). We use this observation to show that the forgetful 2-functor Forget:\mathfrakTan → \mathfrakCat creates and preserves pseudolimits indexed by 1-categories. As an application, this allows us to describe how equivariant descent interacts with the tangent structures on the category of smooth (real) manifolds and on various categories of (algebraic) varieties over a field.