Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E∞ algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of E∞ algebras is faithful but not full.
Coherent functors 𝓢 → Ab from a compactly generated triangulated category into the category of abelian groups are studied. This is inspired by Auslander's classical analysis of coherent functors from a fixed abelian category into abelian groups. We characterize coherent functors and their filtered colimits in various ways. In addition, we investigate certain subcategories of 𝓢 which arise from families of coherent functors.