Constitutive Structures

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

What might be the proper categorical framework to discuss, for
example, the fact that the Real Numbers have constitutive structures
such as additive abelian group, multiplicative abelian group,
topology generated by open intervals, totally ordered infinite set, and so on?
At first one might think of forgetful functors, but then what would
be the category in which Real Numbers is one object among many?
Or, one might say take a category with exactly one object and a
functor to each of the categories of the constitutive structures. This makes
the Real Numbers look like an "element" of the "intersection" of
diverse categories. Then the Complex Numbers or the Hyperreal Numbers
which contain
the Real Numbers as sub-objects in certain ways are "elements" of
other "intersections" of categories. What am I talking about?

Ellis D. Cooper



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