Barker, L.2016-02-082016-02-0820161090-266Xhttp://hdl.handle.net/11693/21925We 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). © 2015 Elsevier Inc.EnglishBurnside ringExponential morphismPrimary 19A22Rational biset functorSecondary 20C15Tornehave morphisms III: the reduced Tornehave morphism and the Burnside unit functorArticle10.1016/j.jalgebra.2015.09.0010021-8693