[Alta-Logic] Peripatetic seminar (22nd Sept.)

[Robin Cockett]

Time: 11:00am, 22nd Sept 2010

Place: ICT 616

Speaker: Jonathan Gallagher

Title: On Categories of Rational Functions.

Abstract: This talk will present the construction of a category of 
rational functions from any commutative rig, ${\sf Rat}({\cal R})$.  
This category of rational functions is naturally a restriction category 
where partiality is given by the "poles" of the rational functions. When 
the rig, ${\cal R}$ is a ring, these categories of rational functions 
are examples of differential restriction categories -- which will be 
defined.  In addition, when the ring is a unique factorization domain 
its category of rational functions has joins which allows, for example, 
the construction of the classical completion and of manifolds.