A Categorical Formulation of Algebraic Geometry
Category Theory
2017-10-24 v1
Abstract
We construct a category, , 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 , 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.
Cite
@article{arxiv.1710.07752,
title = {A Categorical Formulation of Algebraic Geometry},
author = {Bradley M. Willocks},
journal= {arXiv preprint arXiv:1710.07752},
year = {2017}
}