112. Ernst-Schröder-Kolloquium
Fr, 10. Oktober 2025, 16:00 Uhr s.t.
How to Capture and to Formulate Reality
Prof. Dr. Goro Kato
California Polytechnic State University
Reality is sometimes understood as the way it is ,
meaning we are here and now in space-time and simultaneously
thinking. But how do we express this situation in both physical
and cognitive aspects?
We will focus on Leibniz’s Monadology (where we define
the notion of elementary monads). Next we will focus on Plato’s
Theory of Forms , i.e., false shadows appearing upon the
wall of a cave as physical phenomena.
The true reality is omnipresent abstract Forms (which we
define as a constant ur-functor, i.e., an initial object of
temporal topos) as a source of anamnesis, relating to Kant’s
noumenon (Ding-an-Sich).
Technische Universität Darmstadt,
(Mathe-Gebäude, S2|15-244)
112. Ernst-Schröder-Seminar
Sa, 11. Oktober 2025, 10:00 Uhr s.t.
Coherency between Microcosm and Macrocosm in
Terms of Sheaf Theory
Prof. em. Dr. Goro Kato
California Polytechnic State University
After reviewing necessary notions from categories and sheaves,
the Zen of Yoneda based on Yoneda Lemma and Yoneda Embedding is
explained as one assertion.
The axioms for a special kind of topos, called a temporal topos,
are introduced. As applications, quantum phenomena in microcosm,
e.g., the wave-particle duality, quantum entanglement, uncertainty,
etc., are formulated in terms of temporal topos language.
We define the notion of a light-cone of special relativity in
terms of morphisms among objects in a temporal site.
The gravitational effect is also expressed using the language
of temporal topos.
Temporal Topos Theoretic Views of Measurement
Phenomena and Related Issues
Prof. em. Dr. Goro Kato
California Polytechnic State University
It is our view that measurement phenomena occur every moment
from microcosm through macrocosm. The classical physics realm
of macrocosm is deterministic, but the quantum realm is
non-deterministic.
Our purpose is to provide a unified formulation for these two
realms filled with measurement phenomena in terms of temporal
topos methods. Our vision of reality based on temporal topos
theory is described.
Consider the following example. When a (macroscopic entity)
human speaks, not only well-coordinated actions of various
parts of the body are involved, but also microscopic objects,
e.g., brain cells, atoms, and even elementary particles must be
simultaneously coordinated.
Thinking requires brain cells to function; however, it is
thought that triggers the actions of brain cells. We will
formulate this enigma in terms of temporal topos.
Technische Universität Darmstadt,
(Mathe-Gebäude, S2|15-244)
Prof. Dr. Goro C. Kato
Goro C. Kato is a professor emeritus of mathematics at
California Polytechnic State University, San Luis Obispo, CA, USA.
Kato was born in 1948 in Kariya, Japan, and he came to the
United States on a Rotary International Foundation Fellowship.
He earned his Ph.D. in 1979 from the University of Rochester,
Rochester, NY, and his Ph.D. thesis advisor was Professor Saul Lubkin.
Goro Kato's areas of study are
p-adic cohomology and zeta invariants
the theory of D-modules
the temporal topos theory
Kato’s memoir on his visits from 1986 ~ 2008 to the
Institute for Advanced Study, Princeton, NJ, was published
(in Japanese) by Iwanami-Shoten, Tokyo, 2019.
He and his wife, Christine Willis, hava a son Alexander Benkei
Kato-Willis, who is a pianist-composer. Goro Kato's hobbies are
mineral/crystal collecting, composing Haiku and Waka
(Japanese short poems).
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