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Definition of Inverse system
1. Noun. (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. ¹
2. Noun. (category theory) A generalization of the above definition, where groups are replaced by objects, and homomorphisms are replaced by morphisms. ¹
¹ Source: wiktionary.com
Lexicographical Neighbors of Inverse System
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