I have no working knowledge so it might be apart from standard concepts
- Suppose a huge category Univ, which is category of category of sets, Set
- and its relation to projections of variations/manifolds, Proj
- axiom of regularity (foundation) and large cardinal axioms assure limit and inverse limit of Univ in Set
- they could be related to quantum field theory: regularity assures existence of vacuum (ultraviolet cutoff), large cardinals assures existence of universe (infrared cutoff)
- Proj might be also found in quantum measurement: lattice of related observations
- Proj resembles to Univ but generally lacks limits
- Algebra of integrals forms Proj
- See Segal(1965) and its references http://www.ams.org/journals/bull/1965-71-03/S0002-9904-1965-11284-8/
- among references, for relations to operator ring, see introductions in von Neumann(1960) http://press.princeton.edu/titles/6267.html
- Caratheodory(1986) also explored related topics http://www.amazon.com/dp/0828401616
- Univ is a sort of compactification of Proj, but how we compactificate Proj?
- operator ring theory must have distinction between two ways of compactification, one-point and Stone-Cech
- section of infinity on circumstance, or hyperbolization of ellipse, make infinity to integrable, by counting leaves of the tree
- AdS-CFT might be thought as an example of general hyperbolization
- Can we perform hyperbolization simultaneously in both sides, at UV and IR?
- regarding any automorphic forms as "ellipses", what does it mean, existence of their (discrete) hyperbolizations?
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