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# Macquarie University  Department of Mathematics

## Workshop on Categorical Methods in Algebra, Geometry and Mathematical Physics

### Satellite to the StreetFest conference in honour of Ross Street's sixtieth birthday

#### July 18-21 2005, Australian National University, Canberra

Tue, 19 July:  9:00 - 10:00

##### Centres
###### Street, Ross (Macquarie University, Sydney)

\thanks{This is joint work with Brian Day and Elango Panchadcharam.}
%
The centre of a monoid is typical of constructions having higher-dimensional
categorical analogues. The centre of a monoidal category has been studied
extensively with application to low-dimensional topology and quantum group
theory. The point usually was to create commutativity (a braiding) where none
existed. However, the centre of an already braided monoidal category can still
be of interest: even in the case where the monoidal structure is cartesian
product! Conditions under which the centre of a category of functors into a
monoidal category $\mathcal{V}$ is again a category of functors into
$\mathcal{V}$ will be discussed. Some centres will be calculated and the
advantage of having a monoid in a centre will be explained.

Typeset PDF of this abstract.