Categorical generalization of spectral decomposition
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908337253122048 |
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| author | Nishizawa, Koki Ide, Yusuke Tsumagari, Norihiro |
| author_facet | Nishizawa, Koki Ide, Yusuke Tsumagari, Norihiro |
| contents | In this paper, we give several equivalent characterizations for a category with finite biproducts and the sum operation of arrows, and called categories satisfying these semiadditive $\mathbf{C}\mathbf{Mon}$-categories. This allow us to give equivalent structures without directly confirming the existence of biproducts. Moreover, we define a generalized notion of the spectral decomposition in semiadditive $\mathbf{C}\mathbf{Mon}$-categories. We also define the notion of a semiadditive $\mathbf{C}\mathbf{Mon}$-functor that preserves the spectral decomposition of arrows. Semiadditive $\mathbf{C}\mathbf{Mon}$-categories and semiadditive $\mathbf{C}\mathbf{Mon}$-functors include many examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17956 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Categorical generalization of spectral decomposition Nishizawa, Koki Ide, Yusuke Tsumagari, Norihiro Logic in Computer Science In this paper, we give several equivalent characterizations for a category with finite biproducts and the sum operation of arrows, and called categories satisfying these semiadditive $\mathbf{C}\mathbf{Mon}$-categories. This allow us to give equivalent structures without directly confirming the existence of biproducts. Moreover, we define a generalized notion of the spectral decomposition in semiadditive $\mathbf{C}\mathbf{Mon}$-categories. We also define the notion of a semiadditive $\mathbf{C}\mathbf{Mon}$-functor that preserves the spectral decomposition of arrows. Semiadditive $\mathbf{C}\mathbf{Mon}$-categories and semiadditive $\mathbf{C}\mathbf{Mon}$-functors include many examples. |
| title | Categorical generalization of spectral decomposition |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2504.17956 |