*-Autonomous categories in quantum theory

TL;DR

This paper explores *-autonomous categories, their generalizations, and their significance in quantum mathematics, highlighting their role in understanding duality and convolution structures.

Contribution

The paper extends the concept of *-autonomous categories to promonoidal categories, emphasizing their application in quantum mathematics and related fields.

Findings

*Autonomous categories describe duality in monoidal closed categories

Generalization to promonoidal categories broadens applicability

Highlights usefulness in quantum mathematics

Abstract

*-Autonomous categories were initially defined by M. Barr to describe a type of duality carried by many monoidal closed categories. Later they were generalised by the current author to include *-autonomous promonoidal categories. Together, these structures under "convolution" product give a clear indication of the usefulness of *-autonomy in quantum mathematics and related areas.