On 08/03/2015 19:53, F. William Lawvere wrote:
It is difficult to understand "without objects" without any definition of "object".
One could raise an analogous objection to the notion of a "reflexive graph without vertices", defined as an M-set for the 3-element monoid M consisting of the monotone endomorphisms of the poset 0 < 1. While no mention is made of vertices in this definition, an equivalent notion arises in a canonical way by taking the Karoubi envelope of M, yielding a notion of "vertex". "Without vertices" then just means economizing by skipping the step of taking the envelope. Quine wrote "Word and Object". Reasoning analogously as above, what a category theorist would call an object, Quine would call a word. Vaughan Pratt [For admin and other information see: http://www.mta.ca/~cat-dist/ ]