CATEGORIES OF MANUALS

• Main Author: LOCK, PATRICIA FRAZER
• Language: ENG
• Published: ScholarWorks@UMass Amherst 1981
• Subjects: Mathematics
• Online Access: https://scholarworks.umass.edu/dissertations/AAI8118015

A manual of operations is a model for a collection of physical experiments, or a collection of (perhaps overlapping) sample spaces. To understand this theory, it is essential to understand the relations between manuals. Hence, in this dissertation, we study the morphisms (and, more specifically, the interpretations) of manuals. This is followed by an investigation of the categorical properties of the tensor product of two manuals. We define biinterpretations and prove a universal mapping theorem. We then prove that the tensor product is associative, and define, using an inductive limit, an infinite tensor product. In the final chapter, we develop a language and theory that is broad enough to encompass much of the work which has been done under the general title of "quantum logic."