Type: Seminar

Distribution: World

Expiry: 12 Mar 2010

Auth: benw@bari.maths.usyd.edu.au

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.