2023/04/02 by Peter A. Brooksbank, J. F. Maglione, Brooksbank, P. A. +5
Mathematics · Medicine · #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Neurosurgical Procedures and Complications #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2304.00465
openalex publication_date 2023/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Within a category \mathttC, having objects \mathttC0, 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:\mathttC0 × \mathttC0 → [0,∞] with the property that x≅ 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.