For instance: A substantial portion of the mathematical backbone to this approach is drawn from 'Australian category theory', most notably from work by Max Kelly and M. L. Laplaza,[6] Andre Joyal and Ross Street,[7] A. Carboni and R. F. C. Walters,[8] and Steve Lack.
[11] One of the most notable features of categorical quantum mechanics is that the compositional structure can be faithfully captured by string diagrams.
In contrast to earlier axiomatic approaches, which aimed to reconstruct Hilbert space quantum theory from reasonable assumptions, this attitude of not aiming for a complete axiomatization may lead to new interesting models that describe quantum phenomena, which could be of use when crafting future theories.
[29] The DisCoCat framework applies categorical quantum mechanics to natural language processing.
[30] The types of a pregroup grammar are interpreted as quantum systems, i.e. as objects of a dagger compact category.
The grammatical derivations are interpreted as quantum processes, e.g. a transitive verb takes its subject and object as input and produces a sentence as output.