categories: How do Cross-Category Results Relate to Category Theory? - Doctorow

["Osher Doctorow" <osher@ix.netcom.com>]

From: Osher Doctorow, Ph.D. osher@ix.netcom.com, Sunday March 11, 2001
2:02PM

How do cross-category results relate to category theory?  In particular, is
there a *deeper* theory than category theory which crosses different
categories?   I ask this question because I have been following the function
p1(x,y) = 1 + y - x and its n-dimensional generalization pn(x,y) = 1 + y -
Sn/n where Sn = x1 + x2 + ... + xn  and where 0 < = y < = xi < = 1 for i =
1, 2, ..., n (although the inequality can be changed to just y < = xi in
certain categories) not only across categories but branches of mathematics
including probability, mathematical logic, mathematical physics, geometry,
number theory, algebra including especially ring and module theory,
geometric nonlinear functional analysis, etc.   Even p1 alone appears to
have remarkable importance across these fields and others (including
functional differential and integrodifferential equations).  The category
object changes, but the function p1 and the inequality remains, and there is
even a non-function (which can be made into a function with suitable
restrictions) of type y/x --> 1 + y - x which often splits branches of
mathematics down the middle with one branch using y/x and the other using 1
+ y - x in a generalization of the notion of phase differences (solid versus
liquid versus gas versus superfluid versus superconduction types generalized
to rare versus common/frequent events, highly influencing or influenced
versus low influencing/influenced events, zero curvature versus non-zero
curvature events or objects, anomalous versus non-anomalous conditions,
etc.).

Osher Doctorow
Ventura College, etc.