graded category

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 categories with a single object. 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: graded algebra.

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