Alejandro recently conducted a poll on Category Theory(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# LQG and Category Theory

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