Bibliographic Details
| Title: |
Isomorphism invariant metrics |
| Authors: |
Brooksbank, P. A., Maglione, J. F., O'Brien, E. A., Wilson, J. B. |
| Publication Year: |
2023 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Group Theory, Mathematics - Rings and Algebras |
| More Details: |
Within a category $\mathtt{C}$, having objects $\mathtt{C}_0$, it may be instructive to know not only that two objects are non-isomorphic, but also how far from being isomorphic they are. We introduce pseudo-metrics $d:\mathtt{C}_0 \times \mathtt{C}_0 \to [0,\infty]$ with the property that $x\cong y$ implies $d(x,y)=0$. We also give a canonical construction that associates to each isomorphism invariant a pseudo-metric satisfying that condition. This guarantees a large source of isomorphism invariant pseudo-metrics. We examine such pseudo-metrics for invariants in various categories.
Comment: 16 pages |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2304.00465 |
| Accession Number: |
edsarx.2304.00465 |
| Database: |
arXiv |
