Categorification in Representation Theory: Street -- The 2-Functor Rep as Categorification

The fourth meeting of the working group takes place this Friday at 3.30pm in Carslaw
lecture theatre 159.  This week, the speaker is Ross Street.  I hope to see you there.  

"The 2-Functor Rep as Categorification" ----- Classical mathematics deals with
formulas.  Many of these formulas or equations were actually derived from isomorphisms
of structures; this is "decategorification".  "Categorification" was part of category
theory well before this unfortunate term became popular.  It is the idea that some
equation should be lifted to an isomorphism, or sometimes merely a morphism; but then
that morphism generally would be expected to satisfy some constraints.  Physicists call
this equality breaking.  The constraints are again equations (which naturally leads to
higher categorification not to be discussed here).  I shall emphasise how the passage
from a mathematical structure H to its category Rep(H) of representations suggests how
that structure should be categorified.  I also intend to revisit my work with André
Joyal which can be viewed as providing a categorification RGL(q) of J.  A.  Green’s
[Transactions AMS (1955)] construction of a commutative algebra XGL(q) consisting of
characters of complex representations of the general linear groups over the field with q
elements.