inverse limit English

Meaning inverse limit meaning

What does inverse limit mean?

inverse limit noun

— (algebra) A subset of the Cartesian product of all the members of an inverse system, such that a member M of the subset is a sort of “cross section” of the inverse system (as fiber bundle) induced by the morphisms of it. (If i \le j in the indexing poset then f_{ij}:A_j \rightarrow A_i in the inverse system and if a_i \in A_i, a_j \in A_j are components of M then f_{ij}(a_j) = a_i).

— (category theory) a limit