1. Isomorphism invariant metrics
- Author
-
Brooksbank, P. A., Maglione, J. F., O'Brien, E. A., and Wilson, J. B.
- Subjects
Mathematics - Group Theory ,Mathematics - Rings and Algebras - Abstract
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
- Published
- 2023