mathematics free of a blackboard (I. Gelfand and M. Gromov)
martdowd at aol.com
martdowd at aol.com
Sun Mar 14 22:57:17 EDT 2021
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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