American Heritage® Dictionary of the English Language, Fourth Edition
- n. Biology Similarity of external form or appearance but not of structure or origin.
- n. Zoology A resemblance in form between the immature and adult stages of an animal.
- n. Mathematics A transformation of one set into another that preserves in the second set the operations between the members of the first set.
Century Dictionary and Cyclopedia
- n. Mimicry or imitation of one thing by another; adaptive or analogical resemblance, without true homological or morphological similarity; superficial likeness without structural affinity or relationship. Also homomorphy.
- n. algebra A structure-preserving map between two algebraic structures, such as groups, rings, or vector spaces.
- n. biology A similar appearance of two unrelated organisms or structures
GNU Webster's 1913
- n. (Biol.) Same as homomorphy.
- n. (Bot.) The possession, in one species of plants, of only one kind of flowers; -- opposed to
heteromorphism, dimorphism, and trimorphism.
- n. (Zoöl.) The possession of but one kind of larvæ or young, as in most insects.
- n. similarity of form
- homo- + morphism (Wiktionary)
“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.”
“Then T has a model A with the property that for every model B of T there is a unique homomorphism from”
“A homomorphism from structure A to structure B is a function f from dom (A) to dom (B) with the property that for every atomic formula”
“Next, two properties of that system are established: The rational numbers can be embedded into it, in a way that respects the order and the arithmetic operations defined on those numbers (a corresponding field homomorphism exists); and the new system is continuous, or line-complete, with respect to its order.”
“Each of these functions is from a generator set to an algebra and therefore has a unique extension to a homomorphism.”
“Likewise the homomorphism from G to G is an identity function.”
“Moreover, this correspondence is functorial: any Boolean homomorphism is sent to a continuous map of topological spaces, and, conversely, any continuous map between the spaces is sent to a Boolean homomorphism.”
“The key idea is that compositionality requires the existence of a homomorphism between the expressions of a language and the meanings of those expressions.”
These user-created lists contain the word ‘homomorphism’.
A list of words that are odd or words that I have looked up.
Cool technology-related words.
Stuff that comes up all the time at work.
Looking for tweets for homomorphism.