= Rational homotopy type
The <rational homotopy type> of a <simply connected> space is its equivalence class under zigzags of <rational homotopy equivalences>, or equivalently the <homotopy> type of its <rationalization of a topological space>. For the usual finite-type spaces, it is encoded contravariantly by the isomorphism class of the <Sullivan minimal model>. Isomorphic <cohomology> rings determine this type only when additional information, such as <formality of a topological space>, makes the cochain algebra equivalent to the <cohomology> algebra.
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