Summary: Applied Categorical Structures 10: 469480, 2002.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
On the Amnestic Modification of the Category of
State Property Systems
D. AERTS , E. COLEBUNDERS, A. VAN DER VOORDE and
B. VAN STEIRTEGHEM
Department of Mathematics, Brussels Free University, Pleinlaan 2, B-1050 Brussels, Belgium
(Received: 6 July 1999; accepted: 20 November 1999)
Abstract. 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.
Mathematics Subject Classifications (2000): 54A05, 54B30, 81P05.