**The CoACT ****logo**

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.

And do you see the Sydney Harbour Bridge with a sailboat about to go beneath?