inverse system (suomeksi)

Määritelmät:

(lb, en, 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 partial ordering relation, 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.
(lb, en, category theory) A generalization of the above definition, where groups are replaced by objects, and homomorphisms are replaced by morphisms.