Quantum Collections
Operator Algebras
2016-07-20 v2
Abstract
We develop the viewpoint that the opposite of the category of W*-algebras and unital normal *-homomorphisms is analogous to the category of sets and functions. For each pair of W*-algebras, we construct their free exponential, which in the context of this analogy corresponds to the collection of functions from one of these W*-algebras to the other. We also show that every unital normal completely positive map between W*-algebras arises naturally from a normal state on their free exponential.
Keywords
Cite
@article{arxiv.1202.2994,
title = {Quantum Collections},
author = {Andre Kornell},
journal= {arXiv preprint arXiv:1202.2994},
year = {2016}
}
Comments
added an NSF grant number; fixed a typo in the proof of theorem 9.1