对合范畴与幺半群，具有GNS-对应
Involutive Categories and Monoids, with a GNS-correspondence
摘要：
本文发展了对合范畴理论的基础，并表明这类范畴提供了描述对合幺半群的自然环境。证明了对合单子的Eilenberg-Moore代数范畴是对合的，模和向量空间的共轭是其特例。所谓的Gelfand-Naimark-Segal（GNS）结构的核心被确定为对合幺半群和内积上的状态之间的双射对应。这种对应存在于任意的对合范畴中。
英文摘要：
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. The core of the so-called Gelfand-Naimark-Segal (GNS) construction is identified as a bijective correspondence between states on involutive monoids and inner products. This correspondence exists in arbritrary involutive categories.
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