Categories of sets with infinite addition
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910788625629184 |
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| author | Andrés-Martínez, Pablo Heunen, Chris |
| author_facet | Andrés-Martínez, Pablo Heunen, Chris |
| contents | We consider sets with infinite addition, called $Σ$-monoids, and contribute to their literature in three ways. First, our definition subsumes those from previous works and allows us to relate them in terms of adjuctions between their categories. In particular, we discuss $Σ$-monoids with additive inverses. Second, we show that every Hausdorff commutative monoid is a $Σ$-monoid, and that there is a free Hausdorff commutative monoid for each $Σ$-monoid. Third, we prove that $Σ$-monoids have well-defined tensor products, unlike topological abelian groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_15183 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Categories of sets with infinite addition Andrés-Martínez, Pablo Heunen, Chris Category Theory Rings and Algebras We consider sets with infinite addition, called $Σ$-monoids, and contribute to their literature in three ways. First, our definition subsumes those from previous works and allows us to relate them in terms of adjuctions between their categories. In particular, we discuss $Σ$-monoids with additive inverses. Second, we show that every Hausdorff commutative monoid is a $Σ$-monoid, and that there is a free Hausdorff commutative monoid for each $Σ$-monoid. Third, we prove that $Σ$-monoids have well-defined tensor products, unlike topological abelian groups. |
| title | Categories of sets with infinite addition |
| topic | Category Theory Rings and Algebras |
| url | https://arxiv.org/abs/2308.15183 |