injections, surjections, and bijections correspond precisely to monomorphisms, epimorphisms, and isomorphisms, respectively. History The Oxford English Dictionary records the use of the word injection as a noun by S. Mac Lane in Bulletin of the American Mathematical Society (1950), and injective as an adjective by Eilenberg and Steenrod in Foundations of Algebraic Topology (1952). However, it was not until the French Bourbaki group coined the injective-surjective-bijective terminology (both as nouns and adjectives) that they achieved widespread adoption. See also Horizontal line test Injective module Permutation References External links Earliest Uses of Some of the Words of Mathematics: entry on Injection, Surjection and Bijection has the history of Injection and related terms. Basic concepts in set theory Mathematical relations Functions and mappings