Title: Dagger linear monoids in dagger LDCs

Abstract:

Categorical quantum mechanics describes quantum observable as dagger Frobenius Algebra with extra properties in the category of finite-dimensional Hilbert Spaces. In this talk, I will generalize the notion of dagger Frobenius Algebras to dagger linearly distributive categories (dagger-LDCs). We call the dagger Frobenius Algebras in this setting as dagger linear monoids. We observe that in the setting symmetric dagger LDCs, a dagger linear dual gives rise to endomorphism monoids (usually referred to as the pants monoid) for which the multiplication is anti-isomorphic to the dagger of the comultiplication. Finally, we examine the conditions under which the anti-isomorphic pants monoid coincides with the usual pants monoid in a unitary category.