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Groupoidification Made Easy
John C. Baez, Alexander E. Hoffnung, Christopher D. Walker
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 wi…
Infinite-Dimensional Representations of 2-Groups
John C. Baez, Aristide Baratin, Laurent Freidel +1
A "2-group" is a category equipped with a multiplication satisfying laws like those of a group. Just as groups have representations on vector spaces, 2-groups have representations…
Convenient Categories of Smooth Spaces
John C. Baez, Alexander E. Hoffnung
A "Chen space" is a set X equipped with a collection of "plots" - maps from convex sets to X - satisfying three simple axioms. While an individual Chen space can be much worse than…
The Classifying Space of a Topological 2-Group
John C. Baez, Danny Stevenson
Categorifying the concept of topological group, one obtains the notion of a 'topological 2-group'. This in turn allows a theory of 'principal 2-bundles' generalizing the usual theo…