FOM: Definition of Lawvere theory: additional condition needed

Martin Davis martind at
Sun Mar 22 14:18:46 EST 1998

At 09:39 AM 3/21/98 -0800, Vaughan Pratt wrote:

>The difference between graph theory and category theory is that category
>theory incorporates the congruence on paths as part of its structure,
>permitting every instance of "congruent to" to be streamlined to
>"equal to".  The graph theory formulation of category theory is like a
>bicycle with training wheels: great for getting started but eventually
>you want to take off the training wheels so you can go faster.

Dear Vaughan,

Surely this is not the only difference between such utterly different
subjects. It has been noted that the \in relation in a model of set theory
can be thought of as defining a graph. But single sentence of the form: "The
difference between grapg theory and set theory is ..." would just be silly.


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