In
category theory, a branch of mathematics, a
diagram is the categorical analogue of an
indexed family in
set theory. The primary difference is that in the categorical setting one has
morphisms that also need indexing. An indexed family of sets is a collection of sets, indexed by a fixed set; equivalently, a
function from a fixed index
set to the class of
sets. A diagram is a collection of objects and morphisms, indexed by a fixed category; equivalently, a
functor from a fixed index
category to some
category.