/sci/ - Science & Math

>>16220855
Not really. Isomorphism is just contextual equivalence. In the context of metric spaces or Riemannian manifolds, isometries are isomorphisms.
Homotopy/homology equivalence (I don't think I've ever seen homology equivalence be used as an expression, but it's easy to extend the concept) would be weaker, yes, but it's also important to pay attention to whether or not you're just changing the context (strong homotopy equivalences are isomorphisms in the category of topological spaces where you modulo out homotopical continuous maps).