# Idea

Groupoidification is a program based on the observation that the operation of pull-pushing bundles of groupoids

$\begin{array}{c}\Psi \\ ↓\\ X\end{array}$\array{ \Psi \\ \downarrow \\ X }

through spans

$\begin{array}{ccc}& & S\\ & ↙& & ↘\\ X& & & & Y\end{array}$\array{ && S \\ & \swarrow && \searrow \\ X &&&& Y }

of groupoids becomes a linear map acting on vector spaces after taking groupoid cardinality – after “degroupoidification”.

From another perspective, these over-groupoids are an example for geometric function objects as considered in the context of geometric function theory.

# References

John Baez keeps a web page with relevant links and background material

• John Baez Groupoidification (web)

In particular there are the articles in preparation

• John Baez, Alexander Hoffnung, Christopher Walker, Higher-dimensional algebra VII: Groupoidification, arxiv/0908.4305

• John Baez, Alexander Hoffnung, Higher-dimensional algebra VIII: The Hecke Bicategory, (pdf)

# Relation to representation theory

Groupoidification seems to be a central underlying governing principle in representation theory in its incarnation in geometric function theory.

# Relation to quantization

Groupoidification in particular seems to illuminate structures encountered in the context of quantum field theory. Discussions of groupoidification in the context of QFT are

• Jeffrey Morton, Categorified algebra and quantum mechanics, Theory and Application of Categories 16 (2006), 785-854 (arXiv, tac)

• Jeffrey C. Morton, 2-Vector Spaces and Groupoids (arXiv)

Some related remarks are in

Revised on April 7, 2010 17:53:09 by Zoran Škoda (193.55.10.104)