On the Amnestic Modification of the Category of State Property Systems
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State property systems were created on the basis of physical intuition in order to describe a mathematical model for physical systems. A state property system consists of a triple: a set of states, a complete lattice of properties and a specified function linking the other two components. The definition of morphisms between such objects was inspired by the physical idea of a subsystem. In this paper we give an isomorphic description of the category of state property systems, thus introducing a category SP, which is concrete over Set. This isomorphic description enables us to investigate further categorical properties of SP. It turns out that the category SP is not amnestic. In our main theorem we prove that the amnestic modification of SP is the construct Cls of closure spaces and continuous maps. Moreover we observe that the categorical product and coproduct in Cls find, through SP, application in physics.
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