** **

** **

It is recognized among category theorists that the work done by Australian practitioners has a particular flavour and the term "Australian category theory" was coined.

CoACT stands for our Centre of Australian Category Theory. However "coact" is also short for "coaction"; a notion fundamental to our subject. While actions are important and common place in "modern algebra", the idea to reverse arrows and consider coactions is not so natural in that context. Category theory provides the setting with its concept of opposite category. Monoidal categories also lurk where coactions are involved.

Coactions are usually regarded as generalised diagonal operations and so are commonly denoted by the upper case Greek letter delta. Such a delta : M --> MQ might express the right coaction of Q on M; but also M stands for Mathematics and MQ for Macquarie.

The simplexes have played a major role in our work. The 2-dimensional simplex is a triangle. The upper case delta symbolises this connection; it is frequently used to denote the category of model simplexes. Here the arrow reminds us that we are particularly interested in direction; our work involves oriented simplexes.