Pro-isomorphisms of homology towers

ABSTRACT. We find criteria which ensure that two towers of spaces have pro-isomorphic mod p homology towers. In particular, this gives criteria for determining when the homology of an inverse limit is isomorphic to the inverse limit of the homology tower. As a consequence, we establish new conditions for the convergence of the generalized Eilenberg-Moore spectral sequence (i.e. the homology spectral sequence of a cosimplicial space), which computes the homology of inverse limits such as mapping spaces or fibers of fibrations.