Lifting independence along functors
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912560914104320 |
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| author | Kamsma, Mark Rosický, Jiří |
| author_facet | Kamsma, Mark Rosický, Jiří |
| contents | Given a functor $F: \mathcal{C} \to \mathcal{D}$ and a model-theoretic independence relation on $\mathcal{D}$, we can lift that independence relation along $F$ to $\mathcal{C}$ by declaring a commuting square in $\mathcal{C}$ to be independent if its image under $F$ is independent. For each property that an independence relation can have we give assumptions on the functor that guarantee the property to be lifted. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14813 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lifting independence along functors Kamsma, Mark Rosický, Jiří Category Theory Logic 03C45 (Primary), 18C35, 03C95 (Secondary) Given a functor $F: \mathcal{C} \to \mathcal{D}$ and a model-theoretic independence relation on $\mathcal{D}$, we can lift that independence relation along $F$ to $\mathcal{C}$ by declaring a commuting square in $\mathcal{C}$ to be independent if its image under $F$ is independent. For each property that an independence relation can have we give assumptions on the functor that guarantee the property to be lifted. |
| title | Lifting independence along functors |
| topic | Category Theory Logic 03C45 (Primary), 18C35, 03C95 (Secondary) |
| url | https://arxiv.org/abs/2411.14813 |