Tornehave morphisms III: The reduced Tornehave morphism and the Burnside unit functor

We shall show that a morphism anticipated by Tornehave induces (and helps to explain) Bouc's isomorphism relating a quotient of the Burnside unit functor (measuring a difference between real and rational representations of finite 2-groups) and a quotient of the kernel of linearization (measuring a difference between rhetorical and rational 2-biset functors). (C) 2015 Elsevier Inc. All rights reserved.