Simplicial effects and weakly associative partial groups
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913684934098944 |
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| author | Okay, Cihan Castillo, Victor Stern, Walker H. |
| author_facet | Okay, Cihan Castillo, Victor Stern, Walker H. |
| contents | In this paper, we introduce a new category of simplicial effects that extends the categories of effect algebras and their multi-object counterpart, effect algebroids. Our approach is based on relaxing the associativity condition satisfied by effect algebras and, more generally, partial monoids. Within this framework, simplicial effects and weakly associative partial groups arise as two extreme cases in the category of weak partial monoids. Our motivation is to capture simplicial structures from the theory of simplicial distributions and measurements that behave like effects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05958 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simplicial effects and weakly associative partial groups Okay, Cihan Castillo, Victor Stern, Walker H. Category Theory Quantum Physics In this paper, we introduce a new category of simplicial effects that extends the categories of effect algebras and their multi-object counterpart, effect algebroids. Our approach is based on relaxing the associativity condition satisfied by effect algebras and, more generally, partial monoids. Within this framework, simplicial effects and weakly associative partial groups arise as two extreme cases in the category of weak partial monoids. Our motivation is to capture simplicial structures from the theory of simplicial distributions and measurements that behave like effects. |
| title | Simplicial effects and weakly associative partial groups |
| topic | Category Theory Quantum Physics |
| url | https://arxiv.org/abs/2502.05958 |