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 http://ebooks.worldscinet.com/ISBN/9789812779953/9789812779953_0008.html. Journal homepage: http://ebooks.worldscinet.com/ISBN/9789812779953/9789812779953.html.

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