Infinite-Dimensionality in Quantum Foundations: W*-algebras as Presheaves over Matrix Algebras

TL;DR

This paper demonstrates that W*-algebras can be constructed as colimits of matrix algebras, highlighting their dense relationship and providing a new perspective in quantum foundations.

Contribution

It introduces a novel categorical framework representing W*-algebras as presheaves over matrix algebras, emphasizing their infinite-dimensional structure.

Findings

W*-algebras are canonical colimits of matrix algebra diagrams

Matrix algebras are dense in W*-algebras

Provides a new categorical perspective on quantum structures

Abstract

In this paper, W*-algebras are presented as canonical colimits of diagrams of matrix algebras and completely positive maps. In other words, matrix algebras are dense in W*-algebras.