We give a set of foundations for cellular Ek-algebras which are especially convenient for applications to homological stability. We provide con- ceptual and computational tools in this setting, such as filtrations, a homology theory for Ek-algebras with a Hurewicz theorem, CW approximations, and many spectral sequences, which shall be used for such applications in future papers.
Galatius et al. (Wed,) studied this question.