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

[José Manuel Rodríguez Caballero]

Martin Dowd wrote:

> Jose Caballero writes: "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." [end of
> quotation]
>  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.


I agree, it is the same as with the number 3 (this example is easier than
the graph), which can be represented as

representation 1. { { {} } }

representation 2. { {}, {}, {} }

representation 3. { {}, { {} }, { { {} } } }

etc.

On the other hand, the number 3 in category theory seems to be less
dependent on the representation.

Reference to natural number object:
https://ncatlab.org/nlab/show/natural+numbers+object

Kind regards,
Jose M.
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