Some remarks on representations up to homotopy

Abstract

Motivated by the study of the interrelation between functorial and algebraic quantum field theory, we point out that on any locally trivial bundle of compact groups, representations up to homotopy are enough to separate points by means of the associated representations in cohomol- ogy. Furthermore, we observe that the derived representation category of any compact group is equivalent to the category of ordinary (finite- dimensional) representations of the group.