mathematics free of a blackboard (I. Gelfand and M. Gromov)
José Manuel Rodríguez Caballero
josephcmac at gmail.com
Tue Mar 16 19:28:09 EDT 2021
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.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20210316/40d7214f/attachment.html>
More information about the FOM
mailing list