Timeline for The two ways Feynman diagrams appear in mathematics
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 10, 2018 at 22:42 | comment | added | Abdelmalek Abdesselam | Indeed, the paper by Baez and Dolan was one of my sources of inspiration. See bottom of page 10 in the published version of my article. | |
| Jan 10, 2018 at 22:21 | comment | added | Todd Trimble | I wouldn't have thought Grothendieck universes would ever be invited to the party, but anyway I'm glad to see you emphasize underlying combinatorial ideas. As you know, Baez and Dolan looked at species operations to categorify certain aspects of the ladder calculus. I'll be interested to read what you've done in related areas. | |
| Jan 10, 2018 at 20:40 | comment | added | Abdelmalek Abdesselam | ...but these are categories built with finite sets as in Joyal's theory of combinatorial species. See this article: emis.de/journals/SLC/wpapers/s49abdess.html for a development of this idea. An advantage of this kind of reduction to extremely small categories is that one does not have to worry about Grothendieck universes and things like that. | |
| Jan 10, 2018 at 20:36 | comment | added | Abdelmalek Abdesselam | @ToddTrimble: Point taken. I changed wording to "advanced". I agree that the basics of categories are simple. Maybe they should be taught in the undergraduate curriculum. However the matrix algebra point of view that I described is, I think, even more elementary. All one needs is a good understanding of the notation $\sum_{i=1}^{n}$ and some agility with Fubini's Theorem for finite sums. However, even from this elementary angle, when one starts doing more complicated things with diagrams, one needs tools from the theory of categories... | |
| Jan 10, 2018 at 20:32 | history | edited | Abdelmalek Abdesselam | CC BY-SA 3.0 |
added 3 characters in body
|
| Jan 10, 2018 at 19:26 | comment | added | Todd Trimble | Your answer is very much appreciated, but I slightly object to the idea that monoidal closed categories are anything fancy; the concept is simple and commonplace. (Generally, I want people to feel that category theory is accessible and useful and makes life easier, not more complicated.) Same with string diagrams. | |
| Jan 10, 2018 at 19:15 | history | edited | Abdelmalek Abdesselam | CC BY-SA 3.0 |
deleted 7 characters in body
|
| Jan 10, 2018 at 18:49 | history | answered | Abdelmalek Abdesselam | CC BY-SA 3.0 |