Alejandro recently conducted a poll on Category Theory and the response was remarkably positive out of 7 respondents to the question "Do you know what a Category is?" there were 6 who said they could quote the definition from memory. the poll was in the "Isham New Quantization" thread https://www.physicsforums.com/showthread.php?s=&threadid=14371 ------------------------------ A new paper by the Portuguese mathematician Jose Manuel Velhinho updates LQG by giving it a Category Theory formulation. I think it is kind of elegant and maybe more conceptual. It impresses me as more than putting old wine in new bottles (more than a simple act of translation into a new language). Also what he does is not obvious----the Category Theory is not mere glitter----or so it seemed to me. You may judge of this differently. I believe he put some thought into it, and it represents creative mathematics: more than just razzle-dazzle. Jose Manuel Velhinho "On the structure of the space of generalized connections" http://arxiv.org/math-ph/0402060 [Broken] It is a 30 page paper. The first 8 pages are a quick summary of LQG the next 12 are putting LQG into Category Theory terms the last 10 are "Representations of the holonomy algebra" which treats a modern development of LQG due in part to work by Sahlmann and by Lewandowski and Sokolow that we read here at PF a few months back.