Published in International Journal of Computing Anticipatory Systems, Volume 12, January 1, 2002, pages 229-240.
Awareness of a conscious entity can exist without elements; therefore, the general notion of an object of a category is employed. One of the characterization of understanding is: for a given local infonnation (awareness) there exists a global information whose restriction is the given information. For such mental activities, category and sheaf theories are employed to formulate consciousness. We will show that the cohomology (more general precohomology) object, a subquotient object, better represents the essence of a conscious entity than an object itself. We will also give a definition of an observation to fonnulate the collapse of the wave and the wave property.
Originally presented at the Fifth International Conference on Computing Anticipatory Systems (CASYS'01), Liege, Belgium, August 13-18, 2001.