Talk:Monomorphism
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let X → D denote the (continuous) restriction map from a topological space X to a dense subset D
- This doesn't make sense to me. How is this "restriction map" defined? If X = R and D = Q, how is the image of sqrt(2) defined?? I think this might be reversed from the correct formulation: let i : D --> X be the injective inclusion of a dense subset of a space X. Then i is both monic and epic in Top, but only injective as a set function, not surjective (i.e. taking the forgetful functor, it's image is monic is Set, but not epic.)
No, the example can't be backwards. The inclusion map is injective. We are looking for a continuous map which is not injective but still is a monomorphism in the category of topological spaces. However, it is not clear to me that the example works. As you say, is there an example of a space which can be continuous mapped onto a dense subset? Clearly one cannot continuously map R onto Q since Q is disconnected. Do any examples exist? -- Fropuff 03:59, 2005 Apr 1 (UTC)
Sorry, just noticed the example was botched. I removed it and will look for an example elsewhere. - Gauge 08:22, 2 Apr 2005 (UTC)
- Found an example. Cheers, Gauge 08:59, 2 Apr 2005 (UTC)
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I do not see the need for new pages on the notions of strong monomorphism, etc. I would suggest giving the precise definition here and creating redirects from those if necessary. Magidin 05:20, 6 February 2006 (UTC)
[edit] Too technical?
Should the introductory paragraphs be simplified, removing all technical jargon and just explaining the concept before diving in to the technical details? This is an encyclopaedia after all, not a technical manual. Tczuel (talk) 02:11, 19 September 2009 (UTC)
[edit] Where does this fact fit?
In context of polymorphism, monomorphic means the opposite (not genetically different from). Where should this fact go? --134.36.64.135 (talk) 14:07, 27 October 2009 (UTC)
- Where it currently is: at the top of the page, where there is a link directing readers to the page on polymorphism for other uses. Magidin (talk) 14:38, 27 October 2009 (UTC)
[edit] More general setting of category theory
"...a left-cancellative morphism, that is, a map f : X → Y such that..." — but in this generality a morphism is not a map, is it? Boris Tsirelson (talk) 11:05, 2 September 2010 (UTC)
