Extension Monads: Some Structure Theorems
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915434351034368 |
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| author | Bowerman, Danielle Insall, Matt |
| author_facet | Bowerman, Danielle Insall, Matt |
| contents | We investigate the behavior of extension monads, introduced in the 1990s by the second author, in terms of structure results for infinitely many finitary operations and common constructions in varieties or categories of algebras. Specifically, we see that for finite collections of algebras of the same signature there the extension monad operation commutes with the direct product operation, and that the only retractions from an enlargement or extension monad are trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05828 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extension Monads: Some Structure Theorems Bowerman, Danielle Insall, Matt Logic Rings and Algebras 03H05 (Primary) 08A, 18A30, 03C20 (Secondary) We investigate the behavior of extension monads, introduced in the 1990s by the second author, in terms of structure results for infinitely many finitary operations and common constructions in varieties or categories of algebras. Specifically, we see that for finite collections of algebras of the same signature there the extension monad operation commutes with the direct product operation, and that the only retractions from an enlargement or extension monad are trivial. |
| title | Extension Monads: Some Structure Theorems |
| topic | Logic Rings and Algebras 03H05 (Primary) 08A, 18A30, 03C20 (Secondary) |
| url | https://arxiv.org/abs/2508.05828 |