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Jun 16, 2019 at 21:20 comment added Connor Malin @DenisNardin I edited my answer to be more clear.
Jun 16, 2019 at 21:19 history edited Connor Malin CC BY-SA 4.0
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Jun 16, 2019 at 21:12 comment added mme you can forget the notation completely by remembering that $M_f$ is the Mobius band and the map from the circle is the inclusion of the boundary (but of course, the notion of mapping cylinder is independently useful).
Jun 16, 2019 at 20:52 history edited Connor Malin CC BY-SA 4.0
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Jun 16, 2019 at 20:51 comment added Denis Nardin Sorry for the comments, now I got what you mean (you are basically taking a cofibrant replacement of the squaring map). You might want to explain a bit the notation though, because it gave me pause for one moment
Jun 16, 2019 at 20:47 comment added Connor Malin The mapping cylinder. It is homotopy equivalent to the codomain.
Jun 16, 2019 at 20:41 history answered Connor Malin CC BY-SA 4.0