Effect Algebras as Omega-categories
| Autor: | Perticone, Lorenzo, Adams, Robin |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $\omega$-category. We describe explicitly the strict $\omega$-category structure for two classes of operators on a Hilbert space. Comment: 19 pages, 0 figures. Submitted to the 20th International Conference on Quantum Physics and Logic (QPL 2023) |
| Databáze: | arXiv |
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