Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.17257 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We show how an effect algebra $\mathcal{X}$ can be regarded as a category, where the morphisms $x \rightarrow y$ are the elements $f$ such that $x \leq f \leq y$. This gives an embedding $\mathbf{EA} \rightarrow \mathbf{Cat}$. The interval $[x,y]$ proves to be an effect algebra in its own right, so $\mathcal{X}$ is an $\mathbf{EA}$-enriched category. The construction can therefore be repeated, meaning that every effect algebra can be identified with a strict $ω$-category. We describe explicitly the strict $ω$-category structure for two classes of operators on a Hilbert space.