HI - Pavel wrote:
I would like to ask for comments about the history of string diagrams as graphical notation for the arrows of higher and monoidal categories.
There's a lot of history in this paper: John C. Baez and Aaron D. Lauda, A prehistory of n-categorical physics, in Deep Beauty: Mathematical Innovation and the Search for an Underlying Intelligibility of the Quantum World, ed. Hans Halvorson, Cambridge U. Press, Cambridge, 2011, pp. 13-128. Also at https://arxiv.org/abs/0908.2469 The most important people in the early history of string diagrams are Feynman and Penrose, and I give references and a discussion of their key papers. Some of Penrose's papers are a bit hard to find, but he gave me permission to put them here: http://math.ucr.edu/home/baez/penrose/ His approach to constructing space from spin networks (a certain kind of string diagrams) later became part of loop quantum gravity, and I give the story of how that happened, along with the more mathematical side of the story involving the Jones polynomial, the work of Joyal and Street, etc. Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]