By hopf fibration I mean the hopf map: $S^3\to S^2$. I could find references proving that it is a fiber bundle, but I would like to see a proof that it is an actual fibration.
(Here fibration mean that for any space $X$ and homotopy $F : X\times [0,1]\to S^{2}$, whenever $F_0$ has a lift $\tilde{h} : X\to S^{3}$ then $F$ has a lift $\tilde{F} : [0,1]\times S^2\to S^{3}$ with $\tilde{F}_0 = \tilde{h}$)
I'm completely new to fibrations, any reference or highlight of the ideas involved would be appreciated. Thank you.