This paper discusses why the mathematics of quantum theory can also be applied to cognition. Here, “mathematics of quantum theory” refers to noncommutative probability theory, which is defined as studies of noncommutative probability spaces — pairs consisting of a noncommutative algebras and a states. Interestingly, noncommutative probability spaces can be generated from categories. If categorical structures are significant in cognition, it follows that noncommutative probability theory would also be a “mathmatics of cognitive science”.
