A comparison between weakly protomodular and protomodular objects in unital categories
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866908639338430464 |
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| author | García-Martínez, Xabier Montoli, Andrea Rodelo, Diana Van der Linden, Tim |
| author_facet | García-Martínez, Xabier Montoli, Andrea Rodelo, Diana Van der Linden, Tim |
| contents | We compare the concepts of protomodular and weakly protomodular objects within the context of unital categories. Our analysis demonstrates that these two notions are generally distinct. To establish this, we introduce left pseudocancellative unital magmas and characterise weakly protomodular objects within the variety of algebras they constitute. Subsequently, we present an example of a weakly protomodular object that is not protomodular in this category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19076 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A comparison between weakly protomodular and protomodular objects in unital categories García-Martínez, Xabier Montoli, Andrea Rodelo, Diana Van der Linden, Tim Category Theory 18E13, 18E99, 18C05, 08C05 We compare the concepts of protomodular and weakly protomodular objects within the context of unital categories. Our analysis demonstrates that these two notions are generally distinct. To establish this, we introduce left pseudocancellative unital magmas and characterise weakly protomodular objects within the variety of algebras they constitute. Subsequently, we present an example of a weakly protomodular object that is not protomodular in this category. |
| title | A comparison between weakly protomodular and protomodular objects in unital categories |
| topic | Category Theory 18E13, 18E99, 18C05, 08C05 |
| url | https://arxiv.org/abs/2409.19076 |