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Jul 12, 2022 at 19:02 comment added Sebastian Monnet That's very helpful, thank you!
Jul 12, 2022 at 16:47 comment added Dmitri Pavlov @SebastianMonnet: I added an argument for this.
Jul 12, 2022 at 16:47 history edited Dmitri Pavlov CC BY-SA 4.0
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Jul 12, 2022 at 12:48 comment added Sebastian Monnet I know I already accepted the answer, but would you mind expanding on what the elementary argument is that shows we have a functor? The only things I know about the homotopy category are the universal property and the fact that homotopic maps get identified. My understanding of homotopic maps is pretty flimsy though, so I'm not sure if it's obvious that different choices for F(g) are homotopic
Jul 11, 2022 at 23:23 vote accept Sebastian Monnet
Jul 11, 2022 at 21:48 history edited Dmitri Pavlov CC BY-SA 4.0
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Jul 11, 2022 at 21:10 history edited Dmitri Pavlov CC BY-SA 4.0
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Jul 11, 2022 at 21:06 history edited Dmitri Pavlov CC BY-SA 4.0
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Jul 11, 2022 at 21:04 history answered Dmitri Pavlov CC BY-SA 4.0