What is "inverse system"

n. 1 (context algebra English) An indexed family of groups whose index set is a directed poset, together with a set of homomorphisms which are indexed by a subset of the Cartesian product of the index set with itself — which subset corresponds to the partial ordering relation of the directed poset — such that the domain and codomain of each homomorphism is obtained by ''reversing'' its ordered pair of indexes $(e.g.,\; f\_\{i\; j\}\; :\; G\_j\; rightarrow\; G\_i)$, and such that the homomorphisms compose in a way which reflects the reflexivity and transitivity of the order relation. 2 (context category theory English) A generalization of the above definition, where groups are replaced by objects, and homomorphisms are replaced by morphisms.

In mathematics, an inverse system in a category C is a functor from a small cofiltered category I to C. An inverse system is sometimes called a pro-object in C. The dual concept is a direct system.