Effect Algebras as Omega-categories
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911195709046784 |
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| author | Perticone, Lorenzo Adams, Robin |
| author_facet | Perticone, Lorenzo Adams, Robin |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_17257 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Effect Algebras as Omega-categories Perticone, Lorenzo Adams, Robin Logic in Computer Science 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. |
| title | Effect Algebras as Omega-categories |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2303.17257 |