Stubbe, I
Considering the lattice of properties of a physical system, it has been argued elsewhere that-to build a calculus of propositions having a well-behaved notion of disjunction (and implication)-one should consider a very particular frame completion of this lattice. We show that the pertinent frame completion is obtained as sheafification of the presheaves on the given meet-semilattice with respect to its canonical Grothendieck topology, an explicit description of which is easily given. Our conclusion is that there is an intrinsic categorical quality to the notion of "disjunction" in the context of property lattices of physical systems.
- Heller, M., Odrzygozdz, Z., Pysiak, L., and Sasin, W. (2004). Noncommutative unification of general relativity and quantum mechanics. A Finite Model. General Relativity and Gravitation 36, 111–126.
- Heller, M., Pysiak, L., and Sasin, W. (2005). Noncommutative unification of general relativity and quantum mechanics. Available at www.arxiv.org/abs/gr-qc/0504014.
- Madore J., An Introduction to Noncommutative Differential Geometry and its Physical Applications, ISBN:9780511569357, 10.1017/cbo9780511569357
Bibliographic reference |
Stubbe, I. The canonical topology on a meet-semilattice. In: International Journal of Theoretical Physics, Vol. 44, no. 12, p. 2283-2293 (2005) |
Permanent URL |
http://hdl.handle.net/2078.1/38392 |