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Aug 23, 2023 at 1:03 comment added David Roberts @TianVlašić yes, I appreciated that. Bimorphic equivalence of topological spaces seems like a moderately nontrivial problem to consider...
Aug 22, 2023 at 21:58 comment added David Roberts @TianVlašić yes, this is true. But I see I wrote "if...bimorphisms are given by" bijective functions. So it's just a special case.
Aug 22, 2023 at 20:27 comment added Tian Vlašić @DavidRoberts I don't think bimorphisms of concrete categories are the bijective functions. There a are plenty examples of epimorphisms, say in $\mathbf{Ring}$ that are not surjective.
Aug 31, 2010 at 21:31 history edited David Roberts CC BY-SA 2.5
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Aug 31, 2010 at 21:25 comment added David Roberts Not as such, but trying to give something relevant to the question. Perhaps I could have worded it: if you want to look at inequivalent topologies on a set, then you can't looks at isomorphism classes, but at bimorphism classes of spaces.
Aug 31, 2010 at 11:56 comment added Martin Brandenburg To what extent does this answer the question?
Aug 31, 2010 at 2:32 history answered David Roberts CC BY-SA 2.5