English

A Categorical Formulation of Algebraic Geometry

Category Theory 2017-10-24 v1

Abstract

We construct a category, Ω\Omega, 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\Omega, 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.

Keywords

Cite

@article{arxiv.1710.07752,
  title  = {A Categorical Formulation of Algebraic Geometry},
  author = {Bradley M. Willocks},
  journal= {arXiv preprint arXiv:1710.07752},
  year   = {2017}
}
R2 v1 2026-06-22T22:21:11.107Z