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Jan 6, 2017 at 12:52 comment added François Durand Ok, done. Thanks again for your answers.
Jan 6, 2017 at 12:52 history edited François Durand CC BY-SA 3.0
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Jan 6, 2017 at 11:32 comment added Kevin Buzzard Oh! Then I am going to go with "I don't know any particular standard terminology for this kind of object" (and I'd suggest that you edit the question, rather than fixing it in the comments). Maybe someone else can suggest something.
Jan 6, 2017 at 11:20 comment added François Durand Thanks for your suggestion, which makes me realize that I oversimplified a bit my original question. In fact, what I consider exactly is $f_r : X \to Y$ defined by $f_r = f \circ r \circ []$, where the bracket operator takes the equivalence class of an element. For this reason, it seems to me that "restriction" does not convey exactly the notion I'm using.
Jan 6, 2017 at 10:52 comment added Kevin Buzzard Restriction of $f$ to $r$? To give $r$ is to give its image. In fact if you work with the image of $f$ then it's the restriction of $f$ to this image.
Jan 6, 2017 at 10:12 review First posts
Jan 6, 2017 at 10:16
Jan 6, 2017 at 10:12 history asked François Durand CC BY-SA 3.0