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Microcosm to Macrocosm Via the Notion of a Sheaf (Observers in Terms of t-Topos)
Physics of Emergence and Organization
  • Goro Kato, California Polytechnic State University, San Luis Obispo
Publication Date
The fundamental approach toward matter, space and time is that particles (either objects of macrocosm or microcosm), space and time are all presheafified. Namely, the concept of a presheaf is most fundamental for matter, space and time. An observation of a particle is represented by a morphism from the observed particle (its associated presheaf) to the observer (its associated presheaf) over a specified object (called a generalized time period) of a t-site (i.e. a category with a Grothendieck topology). This formulation provides a scale independent and background space-time free theory (since, for the t-topos theoretic formulation, space and time are discretely defined by the associated particle, whose particle-dependency is a consequence of quantum entanglement.). It is our basic scheme that the method of t-topos may provide a device for understanding and concrete formulation of macro-object and micro-object interconnection as morphisms in the sense of t-topos.
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This is an electronic version of an article published in Physics of Emergence and Organization. The definitive version is available at Journal homepage:
Citation Information
Goro Kato. "Microcosm to Macrocosm Via the Notion of a Sheaf (Observers in Terms of t-Topos)" Physics of Emergence and Organization (2008) p. 229 - 232
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