Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.17956 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of 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.