An introduction to compact symmetric multicategories and problematic loops (part 1)

Sophie Raynor – 27 February 2019

A useful and intuitively nice approach to thinking about operad-like structures is in terms of families of graphs that encode their combinatorics. (Martin Markl coined the umbrella term '(operadic) pasting scheme' to systemise this approach.) The idea is very simple, but the details can get quite messy. Joyal and Kock [JK] used a clever definition of graphs to construct a big class of operad-like structures that they called compact symmetric multicategories. Everything in their construction was functorial, and required a minimum of data - but it wasn't quite correct. In this talk, I'll give some context to the story and explain the J-K construction and where it goes wrong. I'll talk about a solution in a following seminar.

[JK] A. Joyal and J. Kock. Feynman graphs, and nerve theorem for compact symmetric multicategories (extended abstract). Electronic Note in Theoretical Computer Science, 270(2):105--113, 2011. Proceedings of the 6th International Workshop on Quantum Physics and Logic (QPL 2009).