Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
- 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 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.
from The Century Dictionary.
- noun 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 .
from the GNU version of the Collaborative International Dictionary of English.
- noun (Biol.) Same as
homomorphy . - noun (Bot.) The possession, in one species of plants, of only one kind of flowers; -- opposed to
heteromorphism ,dimorphism , andtrimorphism . - noun (Zoöl.) The possession of but one kind of larvæ or young, as in most insects.
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- noun algebra A structure-preserving
map between twoalgebraic structures , such asgroups ,rings , orvector spaces . - noun biology A similar
appearance of two unrelated organisms or structures
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
- noun similarity of form
Etymologies
from Wiktionary, Creative Commons Attribution/Share-Alike License
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Examples
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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.
Algebra Pratt, Vaughan 2007
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Then T has a model A with the property that for every model B of T there is a unique homomorphism from
First-order Model Theory Hodges, Wilfrid 2009
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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.
First-order Model Theory Hodges, Wilfrid 2009
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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
First-order Model Theory Hodges, Wilfrid 2009
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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.
First-order Model Theory Hodges, Wilfrid 2009
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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.
Dedekind's Contributions to the Foundations of Mathematics Reck, Erich 2008
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Likewise the homomorphism from G to G is an identity function.
Algebra Pratt, Vaughan 2007
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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.
Category Theory Marquis, Jean-Pierre 2007
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The key idea is that compositionality requires the existence of a homomorphism between the expressions of a language and the meanings of those expressions.
Compositionality Szabó, Zoltán Gendler 2007
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Each of these functions is from a generator set to an algebra and therefore has a unique extension to a homomorphism.
Algebra Pratt, Vaughan 2007
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