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