Graded category - Citizendia

A graded category is a mathematical concept. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and

If $\mathcal{A}$ is a category, then a $\mathcal{A}$ -graded category is a category $\mathcal{C}$ together with a functor $F:\mathcal{C} \rightarrow \mathcal{A}$ . In Mathematics, category theory deals in an abstract way with mathematical Structures and relationships between them it abstracts from sets In Category theory, a branch of Mathematics, a functor is a special type of mapping between categories

Monoids and groups can be thought of categories with a single element. In Abstract algebra, a branch of Mathematics, a monoid is an Algebraic structure with a single Associative Binary operation In Mathematics, a group is a set of elements together with an operation that combines any two of its elements to form a third element In Mathematics, the elements or members of a set (or more generally a class) are all those objects which when collected together make up the A monoid-graded or group-graded category is therefore one in which to each morphism is attached an element of a given monoid (resp. In Mathematics, a morphism is an abstraction derived from structure-preserving mappings between two Mathematical structures The study of morphisms and group), its grade. This must be compatible with composition, in the sense that compositions have the product grade. In Mathematics, a composite function represents the application of one function to the results of another

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