inverse limit

== English == === Noun === inverse limit (plural inverse limits) (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 ≤ j {\displaystyle i\leq j} in the indexing poset then f i j : A j → A i {\displaystyle f_{ij}:A_{j}\rightarrow A_{i}} in the inverse system and if a i ∈ A i {\displaystyle a_{i}\in A_{i}} , a j ∈ A j {\displaystyle a_{j}\in A_{j}} are components of M then f i j ( a j ) = a i {\displaystyle f_{ij}(a_{j})=a_{i}} ). (category theory) a limit ==== Synonyms ==== projective limit ==== Antonyms ==== direct limit ==== Related terms ==== inverse system