Definition of "homomorphism" [ho•mo•mor•phism]

• Biology Similarity of external form or appearance but not of structure or origin. (noun)
• Zoology A resemblance in form between the immature and adult stages of an animal. (noun)
• Mathematics A transformation of one set into another that preserves in the second set the operations between the members of the first set. (noun)

American Heritage(R) Dictionary of the English Language, Fifth Edition. Copyright (c) 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

• "However F also maps functions to homomorphisms, mapping f to its unique extension as a homomorphism, while U maps homomorphisms to functions, namely the homomorphism itself as a function."
• "We can define an equivalence relation on the domain of a product C, and then take a structure D whose elements are the equivalence classes; the predicate symbols are interpreted in D so as to make the natural map from dom (C) to dom (D) a homomorphism."
• "If it is onto, then the inverse map from dom (B) to dom (A) is also a homomorphism, and both the embedding and its inverse are said to be isomorphisms."