Title: Complementarity in dagger linearly distributive categories

Abstract: Complementarity is key feature that distinguishes quantum from classical mechanics. Two physical variables are complementary if measurement of one variable leads to maximum uncertainty about the value of the other, and vice versa. Algebraically, complementarity is described as two commutative dagger Frobenius Algebras interacting by the Hopf Law in a dagger symmetric monoidal category. The goal of this talk to set up complementarity within the framework of dagger linearly distributive categories. As an example of our algebraic description of complementarity in this setting, I will show that splitting certain kind of idempotents on exponential modalities (! and ?) gives rise to complementary observables.