Meet The Opetopes
Thursday, MR9, 4pm
My talk will centre on a new graphical representation for a familty of geometric objects called the opetopes. It will be a summary of material presented in the paper "Polynomial Functors and Opetopes" by Kock, Batanin, Joyal and Mascari.
To motivate the opetopes, it is useful to understand what a weak n-category is. John Baez's introduction is a good place to start. Baez's introduction provides the motivation for studying opetopic cell shapes (page 18 onwards) and has some nice pictures. Here are some 2-opetopes:
and here is a 3-opetope:
an n-opetope can be naturally depicted as a shape in n-dimensional euclidean space. Since we live in 3-dimensional space, this makes it very difficult to draw (or indeed to represent at all!) opetopes of arbitrarily high dimension.
Joyal et al have found a solution to this in their paper: they propose a new representation of an opetope as a zoom complex, which is something that looks like this:
Hopefully my talk will be understandable to anyone who has taken the part III category theory course - if you haven't, then you should find out what a monad is - and will be mostly conceptual in nature.