The combinatorial model for the Sullivan functor on simplicial sets

We verify the assertion made by Sullivan at the 1974 ICM congress, and previously in print, in Appendix G of the seminal paper “Differential Forms and the Topology of Manifolds” in 1973, that the rational de Rham algebra APL(K) of a finite simplicial complex K has an explicit and direct combinatorial description which is closely related to that of the Stanley-Reisner face ring of K.