# inverse-system

Noun

(*plural* inverse systems)

- (algebra) 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 ordering relation of the directed poset — such that the domain and codomain of each homomorphism is obtained by
*reversing*its ordered pair of indexes , and such that the homomorphisms compose in a way which reflects the reflexivity and transitivity of the order relation. - (category theory) A generalization of the above definition, where groups are replaced by objects, and homomorphisms are replaced by morphisms.