DOI: 10.4153/s0008439526102549 ISSN: 0008-4395

Epimorphism classes and relatively maximal metrics in large-scale geometry

Robert Tang
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Abstract

We consider epimorphisms and several variant notions – split, effective, regular, strong, and extremal – and determine which of these coincide in the metric coarse and coarsely Lipschitz categories. In particular, we characterize extremal epis in the coarsely Lipschitz category via a relative maximality condition on the codomain metric; this can be viewed as a morphism-relative analog of Rosendal’s maximal metrics for topological groups.

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