Natural Functorial Categorical Intuition

["Ellis D. Cooper" <xtalv1@netropolis.net>]

My motto has been "Rigor cleans the window through which intuition
shines." It seems to me that
a great deal more is known about mathematical rigor than about
mathematical intuition.

Economics Nobelist Daniel Kahneman recently published at www.edge.org
a survey of several
men-decades of research on flaws of human statistical intuition. A
paper, "The Intuitive Experience" in
"The View from Within" (Journal of Consciousness Studies, V.6 1999)
discusses in considerable
detail schema and methods of invocation of intuition in
psychotherapy, art, and biology research.

My overall question is whether there really are different kinds of
intuition depending on the research
discipline. In particular, is there some kind of kinetic intuition
specific to category theory that crucially
involves visualization of time-varying diagrams? Do conjectured
adjoint functors arise from distinct algebraic, or
geometric, or logical intuitions? Do categorists deploy special
methods to access their intuition, or
do intuitions just happen to those with a knack for category theory?
Does categorical intuition just
develop with experience, or is there a specialized training to
enhance it? Is categorical intuition
any different from mathematical intuition in general?

Ellis D. Cooper



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