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Higher-Dimensional Algebra VII: Groupoidification
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…
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…
From Loop Groups to 2-Groups
John C. Baez, Alissa S. Crans, Danny Stevenson +1
We describe an interesting relation between Lie 2-algebras, the Kac-Moody central extensions of loop groups, and the group . A Lie 2-algebra is a categorified v…
Higher-Dimensional Algebra VI: Lie 2-Algebras
John C. Baez, Alissa S. Crans
The theory of Lie algebras can be categorified starting from a new notion of "2-vector space", which we define as an internal category in Vect. There is a 2-category 2Vect having t…
Higher-Dimensional Algebra V: 2-Groups
John C. Baez, Aaron D. Lauda
A 2-group is a "categorified" version of a group, in which the underlying set G has been replaced by a category and the multiplication map has been replaced by a functor. Various v…
From Finite Sets to Feynman Diagrams
John C. Baez, James Dolan
`Categorification' is the process of replacing equations by isomorphisms. We describe some of the ways a thoroughgoing emphasis on categorification can simplify and unify mathemati…
Higher-Dimensional Algebra IV: 2-Tangles
John C. Baez, Laurel Langford
Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R^4 can be described a…
Categorification
John C. Baez, James Dolan
Categorification is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between fu…