In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. (Def: http://en.m.wikipedia.org/wiki/Higher_category_theory)

In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. Reference: Wikipedia.

Topics (between others): Strict higher categories, Weak higher categories, Quasi-categories.