arXiv subjects

Bradley M. Willocks

Publications and source records attributed to Bradley M. Willocks.

2 recordsLinked to original sources

arXiv2019

Enriched Sets and Higher Categories

We introduce the notion of an enriched set, as an abstraction of enriched categories, and a category of enriched sets. The set of enriched sets is itself described as a set enriched over the category of enriched sets. We introduce a method for the construction of sets enriched over the set of enriched sets from a given enriched set with some addition data, and for "functors" from such enriched sets as should thereby arise to the enriched set of enriched sets.

math.CT↗

arXiv2017

A Categorical Formulation of Algebraic Geometry

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.

math.CT↗