2017/10/21 by Bradley M. Willocks, Willocks, Bradley M.
Mathematics · #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.CT
paper · pdf · doi:10.48550/arxiv.1710.07752
arxiv created 2017/10/21 · openalex publication_date 2017/10/21 · arxiv updated 2017/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a category, Ω, of which the objects are pointed categories and the arrows are pointed correspondences. The notion of a "spec datum" is introduced, as a certain relation between categories, of which one has been given a Grothendieck topology. A "geometry" is interpreted as a sub-category of Ω, and a formalism is given by which such a subcategory is to be associated to a spec datum, reflecting the standard construction of the category of schemes from the category of rings by affine charts.