Categories of vector spaces and Grassmannians

TL;DR

This paper introduces a new categorical framework that unifies vector spaces and Grassmannians, enabling classification of vector bundles and connecting to topological K-theory.

Contribution

It constructs a novel category encompassing vector spaces and Grassmannians, linking bundle classification to topological K-theory spectrum.

Findings

Unified category of vector spaces and Grassmannians

Classifies vector bundles and bundle isomorphisms

Connects to topological K-theory spectrum

Abstract

We construct a new category of vector spaces which contains both the standard category of vector spaces and Grassmannians. Its space of objects classifies vector bundles, its space of morphisms classifies bundle isomorphisms, and it can be delooped to obtain the topological $K$-theory spectrum.