## Categorification (1997)

Venue: | Contemporary Mathematics 230. American Mathematical Society |

Citations: | 4 - 1 self |

### BibTeX

@INPROCEEDINGS{Baez97categorification,

author = {John C. Baez and James Dolan},

title = {Categorification},

booktitle = {Contemporary Mathematics 230. American Mathematical Society},

year = {1997},

pages = {1--36}

}

### OpenURL

### Abstract

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 isomorphisms between functors, which in turn should satisfy certain equations of their own, called ‘coherence laws’. Iterating this process requires a theory of ‘n-categories’, algebraic structures having objects, morphisms between objects, 2-morphisms between morphisms and so on up to n-morphisms. After a brief introduction to n-categories and their relation to homotopy theory, we discuss algebraic structures that can be seen as iterated categorifications of the natural numbers and integers. These include tangle n-categories, cobordism n-categories, and the homotopy n-types of the loop spaces Ω k S k. We conclude by describing a definition of weak n-categories based on the theory of operads. 1