 Sullivan fibre-model theorem

For a map $f:E\to B$ with simply connected base and the usual finite-type hypotheses, choose a relative Sullivan algebra $M(B)\to M(B)\otimes \Lambda W$ modelling the path-space fibration, with acyclic total algebra. Tensor it over $M(B)$ with a model of $E$ via $f^{\ast }$. The resulting algebra models the homotopy fibre. Relative Sullivan extensions are cofibrant replacements, so this tensor product computes the derived algebraic pushout, contravariantly corresponding to the topological homotopy pullback. Linear differential pairs must be cancelled before reading rational homotopy groups from generators.