From Finite Sets to Feynman Diagrams (2001)
John C. Baez, James Dolan, Björn Engquist, Wilfried Schmid
‘Categorification ’ is the process of replacing equations by isomorphisms. We describe some of the ways a thoroughgoing emphasis on categorification can simplify and unify mathematics. We begin...
From Finite Sets to Feynman Diagrams (2000)
John C. Baez, James Dolan, Bjorn Engquist, Wilfried Schmid
`Categorication' is the process of replacing equations by isomorphisms. We describe some of the ways a thoroughgoing emphasis on categorication can simplify and unify mathematics. We begin with...
Categorification is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between functions by natural...
John C. Baez and James Dolan (1998)
We give a definition of weak n-categories based on the theory of operads. We work with operads having an arbitrary set S of types, or `S-operads', and given such an operad O, we denote its set...
Higher-Dimensional Algebra III: n-Categories and the Algebra of Opetopes (1997)
We give a definition of weak n-categories based on the theory of operads. We work with operads having an arbitrary set S of types, or `S-operads', and given such an operad O, we denote its set...
Higher-Dimensional Algebra and Topological Quantum Field Theory (1995)
The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of...