Higher-Dimensional Algebra VII: Groupoidification

Understand

Groupoidification is a form of categorification in which vector spaces are replaced by groupoids, and linear operators are replaced by spans of groupoids.

• We introduce this idea with a detailed exposition of "degroupoidification": a systematic process that turns groupoids and spans into vector spaces and linear operators.
• Then we present three applications of groupoidification.
• The first is to Feynman diagrams.