I have two homotopies: $f\simeq f'$ and $y\simeq y'$. How can I show that $fy\simeq f'y'$ is again a homotopy?
2026-05-15 21:58:02.1778882282
How to show that homotopy is preserved after composition?
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Hint: First write down the definitions for what it means for $f$ and $f'$ ($y$ and $y'$) to be homotopic, i.e. that there are functions $H$, $G$ defined on source$\times$interval such that [...]. Then try to combine them in a meaningful way.