Involutive Categories and Monoids, with a GNS-Correspondence

Foundations of Physics 42 (7):874-895 (2012)
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Abstract

This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of Eilenberg-Moore algebras of involutive monads are involutive, with conjugation for modules and vector spaces as special case. A part of the so-called Gelfand–Naimark–Segal (GNS) construction is identified as an isomorphism of categories, relating states on involutive monoids and inner products. This correspondence exists in arbritrary involutive symmetric monoidal categories.

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Dagger Categories of Tame Relations.Bart Jacobs - 2013 - Logica Universalis 7 (3):341-370.

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References found in this work

Category Theory.Steve Awodey - 2006 - Oxford, England: Oxford University Press.
Category Theory.[author unknown] - 2007 - Studia Logica 86 (1):133-135.
Dagger Categories of Tame Relations.Bart Jacobs - 2013 - Logica Universalis 7 (3):341-370.
Book Reviews. [REVIEW]B. Jacobs - 2001 - Studia Logica 69 (3):429-455.

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