2025/10/20 by Roy Magen, Magen, Roy
Mathematics · #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
paper · pdf · doi:10.48550/arxiv.2510.17702
openalex publication_date 2025/10/20 · openalex created_date 2025/10/22 · openalex updated_date 2026/07/28
In this article, we introduce fundamental notions and results about pullback formalisms, building on work of Drew-Gallauer. Our main application is producing a pullback formalism SHhol that encodes a version of motivic homotopy theory for complex analytic stacks, and establishing some of its properties. The notions introduced in this article will be used in later articles in which we also establish more properties of SHhol, notably the gluing property of Morel and Voevodsky, the structure of a 6-functor formalism, and a realization map from the motivic homotopy theory of algebraic stacks defined by Khan-Ravi that is compatible with Grothendieck's six operations, generalizing Ayoub's results on Betti realization for schemes.