mathematics free of a blackboard (I. Gelfand and M. Gromov)

[martdowd at aol.com]

FOM,
Jose Caballero writes:
 

n my suggestion framework, category theory is about the abstract graph, whereas set theory is about a particular representation of this graph that can be transformed into other representations.
 
 According to "strict" standards of the set-theoretic foundations, there is no such thing as the abstract graph.  It must be represented somehow as a set, even though it exists independently as an abstract object.
By this criterion, a "large" category, even though it is "informally" given as a tuple of classes, must be "coded" as a single class.  A "concrete" large category can be defined as one where the coding satisfies certain restrictions.  Foe example, an object might be required to be a pair <0,x>, representing the set x, which in turn might code some mathematical object in a standard manner.

Martin Dowd
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