Finite Functorial Semi-Norms and Representability

Abstract

Functorial semi-norms are semi-normed refinements of functors such as singular (co)homology. We investigate how different types of representability affect the (non-)triviality of finite functorial semi-norms on certain functors or classes. In particular, we consider representable functors, generalized cohomology theories, and so-called weakly flexible homology classes in singular homology and l(1)-homology.