Australian Category Theory
Posted by John Baez
The prowess of Australians in higher category theory is renowned worldwide. They’re way ahead of us. If you don’t know what I’m talking about, read this:
 Ross Street, An Australian conspectus of higher category theory, to appear in the proceedings of nCategories: Foundations and Applications, eds. J. Baez and P. May.
For example, check out the fun story on page 4 where an Australian student, asked if he knew the definition of a topological space, correctly but incomprehensibly replied:
Yes, it is a relational βmodule!
So, it behooves the rest of us to watch what they’re up to down under. For this reason, I plan to occasionally post comments to this article, announcing talks at the Australian Category Seminar. I won’t be obsessively systematic, so I apologize in advance for everyone’s talks that I forget to announce.
You can easily spot new comments by looking under “Recent Comments” on the right side of this blog. We engage in a lot of protracted discussions, so that’s a handy feature.
 Simona Paoli, Semistrictification of Tamsamani’s weak 3groupoids: the non pathconnected case. Wednesday October 11, 2006.

Dorette Pronk, Bicategories of fractions II, Wednesday October 11, 2006.
Abstract: In 1967, Gabriel and Zisman introduced the conditions needed on a class of arrows to admit a calculus of fractions. If one has a category $C$ with a class $W$ of weak equivalences that satisfy these conditions, the arrows in the homotopy category of fractions $C[W^{1}]$ can be described as spans where the left leg is in $W$. This category is the universal category obtained from $C$ by inverting the arrows in $W$.
In this talk I will discuss the bicategorical generalization of this: I will discuss the conditions needed for a bicalculus of fractions and give an explicit description of the 2cells in $C[W^{1}]$, the free bicategory obtained by turning the arrows in W into equivalences. This talk is based on my paper in Compositio Mathematica from 1996, but I will discuss some minor improvements on that paper as well as ways to generalize this further to monoidal bicategories of fractions, and eventually, tricategories of fractions.
Re: Australian Category Theory
Kea has fascinating youarethere posts on maths in Australia.