Maps between CW-complexes that induce isomorphisms on all homotopy groups are actually homotopy equivalences.
Whitehead's Theorem
See also
CW-Complex, Homotopy Group, IsomorphismExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Whitehead's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WhiteheadsTheorem.html