Isomorphism invariant metrics
| Autor: | Brooksbank, P. A., Maglione, J. F., O'Brien, E. A., Wilson, J. B. |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 |
| Databáze: | arXiv |
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