= Rational homotopy equivalence
A map between <simply connected> spaces is a <rational homotopy equivalence> when it induces isomorphisms $\pi_n(X)\otimes\mathbb Q\to\pi_n(Y)\otimes\mathbb Q$ in every degree. Equivalently it induces an equivalence of their rationalizations, or a <rational homology> isomorphism by the <rational Whitehead theorem>. Spaces have the same <rational homotopy type> when they are connected by a zigzag of such maps. This is distinct from <rational homotopy equivalence> of algebraic cycles.
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