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Index set

In mathematics, an index set I is another name for a function domain. A collection indexed by I, often written Ai for i in I (can be said 'for i running over I ') is in effect a function A(i) into some codomain.

Index sets are often used in sums (sigma notation) and other such operations; and are common when the Ai are themselves sets rather than numbers, in indexed intersections and unions.

More generally, a functor can be considered as giving rise to an indexed family of objects in a category D, indexed by another category C, and related by morphisms depending on two indices.