Hey I feel like I understand the concept of two spaces being homotopic and I can "visualize" the concept because I think of one space kind of continuously morphing in to the other. But when it comes to thinking of homotopy between functions, I have a harder time. I was trying to think of a way to visualize things and the way I know to visualize a function is by looking at its mapping cylinder. So I was wondering, is it the case that if we can show the mapping cylinders of two functions are homotopic, that the functions themselves are homotopic?(adsbygoogle = window.adsbygoogle || []).push({});

Does anyone have any good resources on things I can read that will help me understand homotopy between functions a little more intuitively? Or to understand the "link" between spaces being homotopic and functions being homotopic

(I know the definitions, but I guess I just have a hard time visualizing functions being homotopic :( )

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# If two functions are homotopic must their mapping cylinders be also?

Can you offer guidance or do you also need help?

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