An algebraic model for the loop space homology of a homotopy fiber

Let F denote the homotopy fiber of a map f : K → L of 2-reduced simplicial sets. Using as input data the strongly homotopy coalgebra structure of the chain complexes of K and L , we construct a small, explicit chain algebra, the homology of which is isomorphic as a graded algebra to the homology of GF , the simplicial (Kan) loop group on F . To construct this model, we develop machinery for modeling the homotopy fiber of a morphism of chain Hopf algebras.