Noun

(*plural* inverse limits)

- (algebra) A subset of the Cartesian product of all the groups of an inverse system, which subset is determined by the following criteria: (1) that, given that each element of the subset is itself a directed poset of "projected" group elements, that if any two such projected group elements relate through the ordering relation, then the "smaller" element should be a homomorphic projection of the "larger" element, where the homomorphism is the corresponding one from the inverse system; (2) that the subset be the largest one for which all of its elements satisfy the preceding property.
- (category theory) The categoretic generalization of the previous definition, where groups become objects, homomorphisms become morphisms, and the second condition becomes the universal property. The Cartesian product becomes the vertex of a particular cone which is the limit.