Graded category

From Wikipedia, the free encyclopedia
Jump to: navigation, search

A graded category is a mathematical concept.

If \mathcal{A} is a category, then a \mathcal{A}-graded category is a category \mathcal{C} together with a functor F:\mathcal{C} \rightarrow \mathcal{A}.

Monoids and groups can be thought of as categories with a single element. A monoid-graded or group-graded category is therefore one in which to each morphism is attached an element of a given monoid (resp. group), its grade. This must be compatible with composition, in the sense that compositions have the product grade.

See also[edit]