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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Sheaf Cohomology Of Conscious Entity, Goro Kato
Sheaf Cohomology Of Conscious Entity, Goro Kato
Mathematics
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 …
Category Theory And Consciousness, Goro Kato, Daniele C. Struppa
Category Theory And Consciousness, Goro Kato, Daniele C. Struppa
Mathematics
No abstract provided.
Orbifold Homeomorphism And Diffeomorphism Groups, Joseph E. Borzellino, Victor Brunsden
Orbifold Homeomorphism And Diffeomorphism Groups, Joseph E. Borzellino, Victor Brunsden
Mathematics
In this paper we outline results on orbifold diffeomorphism groups that were presented at the International Conference on Infinite Dimensional Lie Groups in Geometry and Representation Theory at Howard University, Washington DC on August 17-21, 2000. Specifically, we define the notion of reduced and unreduced orbifold diffeomorphism groups. For the reduced orbifold diffeomorphism group we state and sketch the proof of the following recognition result: Let O1 and O2 be two compact, locally smooth orbifolds. Fix r ≥ 0. Suppose that Φ : Diffr (O1) → Diffr (O2) is a group isomorphism. Then Φ is induced by redred a (topological) …
The Continuum Problem, John Stillwell