Dagger linear logic for categorical quantum mechanics

Categorical quantum mechanics exploits the dagger compact closed structure of finite dimensional Hilbert spaces, and uses graphical calculus string diagrams to facilitate reasoning about processes. A significant portion physics, however, involves infinite processes, it is well-known that category all spaces not closed. Thus, a limitation using categories one cannot directly accommodate natural categorical generalization categories, in which can be modelled, *-autonomous and, more generally, linearly distributive categories. This article starts development this direction generalizing mechanics. An important first step establish behaviour these general settings. notes simultaneously develop semantics multiplicative linear logic. The end with definition mixed unitary category. It subsequently used extend key features