Multicategory

In mathematics (especially category theory), a multicategory is a generalization of the concept of category that allows morphisms of multiple arity. If morphisms in a category are viewed as analogous to functions, then morphisms in a multicategory are analogous to functions of several variables. Multicategories, are also sometimes called operads, or colored operads.

A (non-symmetric) multicategory consists of

Additionally, there are composition operations: Given a sequence of sequences ${\displaystyle ((X_{ij})_{i\in n_{j}})_{j\in m}}$ of objects, a sequence ${\displaystyle (Y_{i})_{i\in m}}$ of objects, and an object Z: if

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