TITLE: Who introduced direct limits?
QUESTION [28 upvotes]: The general notion of a direct limit of a commuting system of embeddings, indexed by pairs in a directed set, has seen heavy use in set theory.  It is the same notion as in category theory.  I was surprised to find that the general definition does not appear in the book on model theory by Chang and Keisler (MR1059055).  Who was the originator of this idea?

REPLY [27 votes]: The definition of a direct limit of groups was given by Pontrjagin in his 1931 paper Über den algebraischen Inhalt topologischer Dualitätssätze