%0 Generic %1 baez1997introduction %A Baez, John C. %D 1997 %K category_theory mathematics %T An Introduction to n-Categories %U http://arxiv.org/abs/q-alg/9705009 %X An n-category is some sort of algebraic structure consisting of objects, morphisms between objects, 2-morphisms between morphisms, and so on up to n-morphisms, together with various ways of composing them. We survey various concepts of n-category, with an emphasis on `weak' n-categories, in which all rules governing the composition of j-morphisms hold only up to equivalence. (An n-morphism is an equivalence if it is invertible, while a j-morphism for j < n is an equivalence if it is invertible up to a (j+1)-morphism that is an equivalence.) We discuss applications of weak n-categories to various subjects including homotopy theory and topological quantum field theory, and review the definition of weak n-categories recently proposed by Dolan and the author.

@misc{baez1997introduction, abstract = {An n-category is some sort of algebraic structure consisting of objects, morphisms between objects, 2-morphisms between morphisms, and so on up to n-morphisms, together with various ways of composing them. We survey various concepts of n-category, with an emphasis on `weak' n-categories, in which all rules governing the composition of j-morphisms hold only up to equivalence. (An n-morphism is an equivalence if it is invertible, while a j-morphism for j < n is an equivalence if it is invertible up to a (j+1)-morphism that is an equivalence.) We discuss applications of weak n-categories to various subjects including homotopy theory and topological quantum field theory, and review the definition of weak n-categories recently proposed by Dolan and the author.}, added-at = {2016-08-14T01:18:34.000+0200}, author = {Baez, John C.}, biburl = {https://www.bibsonomy.org/bibtex/26620bba6effd007de4572df91d74b24b/iblis}, description = {[q-alg/9705009] An Introduction to n-Categories}, interhash = {585d38ba0d895ec11da8adaf7823e297}, intrahash = {6620bba6effd007de4572df91d74b24b}, keywords = {category_theory mathematics}, note = {cite arxiv:q-alg/9705009Comment: 34 pages LaTeX, 30 encapsulated Postscript figures, 2 style files}, timestamp = {2016-08-14T01:18:34.000+0200}, title = {An Introduction to n-Categories}, url = {http://arxiv.org/abs/q-alg/9705009}, year = 1997 }