Data and conditions constitute a presentation. The graph, diagrams, cones & cocones of a sketch are a presentation. This idea has not been superseded, not at all, but it has been completed (in two senses) by the concept of theory, which is the object generated by the presentation: The theory of a sketch, the classifiying topos, the algebraic theory in the sense of Lawvere, and so on. This object contains all the information about any model. That idea is in some way the other face of, or the complementary point of view about, data and conditions. Charles On Fri, May 25, 2012 at 6:09 PM, Ellis D. Cooper <xtalv1@netropolis.net>wrote:
In the 1952 document at http://mathdoc.emath.fr/**archives-bourbaki/PDF/nbt_029.**pdf<http://mathdoc.emath.fr/archives-bourbaki/PDF/nbt_029.pdf>the only mathematician "pr\'{e}sent" referenced by first name only is Sammy.
I was permitted to audit a graduate course on category theory guided by Sammy at Columbia University in the early 1960s. I recall his insistence that mathematical structure is given by data and conditions. Is that idea implicit or explicit in Bourbaki? Has that idea been superceded? How does it relate to the development of algebraic theories as understood by Lawvere, Linton, Barr-Wells, the Elephant, and so on?
Ellis D. Cooper
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]