# FOM: Definition of Lawvere theory: additional condition needed

Martin Davis martind at cs.berkeley.edu
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.

Martin