What is "inverse limit"

n. 1 (context algebra English) 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. 2 (context category theory English) 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.

In mathematics, the inverse limit (also called the projective limit or limit) is a construction that allows one to "glue together" several related objects, the precise manner of the gluing process being specified by morphisms between the objects. Inverse limits can be defined in any category.