[Alta-Logic] Peripatetic talk this Wed.

[Robin Cockett]

Our first talk of the season.
 
If you never understood division by zero by the end of this talk by 
Jonathan there will be absolutely no hope!

If you volunteered to talk you will are likely to be scheduled when we meet!

-robin

Place: ICT 616

Time: 11:00am, Wed 5th October 2011

Speaker: Jonathan Gallagher

Title: "The weak fraction construction"

Abstract: 
In this talk, the construction of fractions will be revisited: The 
fractional equivalence $\frac{a}{a} \sim 1$ will be a replaced by a 
weaker equivalence: $\frac{a}{a2} \sim \frac{1}{a}$.  This weaker 
equivalence has a number of impacts on the operations one expects of 
fractions, and requires us to use weaker structures than commutative 
rigs: called weak commutative rigs.  This fraction construction will be 
shown to be a monad on the category of weak commutative rigs.  The 
category of algebras for this monad will also be developed, and from 
this category of algebras we will build the partial map category with 
respect to 'localizations' to obtain a very general category of rational 
functions.  A series of adjunctions relates this general category of 
rational functions to the partial map category of commutative rings with 
respect to localizations.