Higher-Dimensional Algebra VII: Groupoidification (2009)
Baez, John C., Hoffnung, Alexander E., Walker, Christopher D.
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...
Groupoidification Made Easy (2008)
Baez, John C., Hoffnung, Alexander E., Walker, Christopher D.
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...
Categorified Symplectic Geometry and the Classical String (2008)
Baez, John C., Hoffnung, Alexander E., Rogers, Christopher L.
A Lie 2-algebra is a "categorified" version of a Lie algebra: that is, a category equipped with structures analogous those of a Lie algebra, for which the usual laws hold up to isomorphism. In the...
Convenient Categories of Smooth Spaces (2008)
Baez, John C., Hoffnung, Alexander E.
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 a smooth manifold,...