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

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
Keywords Involution  Monoidal category  Inner products  Gelfand–Naimark–Segal
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DOI 10.1007/s10701-011-9595-7
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References found in this work BETA

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.
Categorical Logic and Type Theory.B. Jacobs - 2001 - Studia Logica 69 (3):429-431.

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

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