A noun is a type of word the meaning of which determines reality. Nouns provide the names for all things: people, objects, sensations, feelings, etc.
WHAT DOES MONOMORPHISM MEAN IN ENGLISH?
In the context of abstract algebra or universal algebra, a monomorphism is an injective homomorphism. A monomorphism from X to Y is often denoted with the notation. In the more general setting of category theory, a monomorphism is a left-cancellative morphism, that is, an arrow f : X → Y such that, for all morphisms g1, g2 : Z → X, Monomorphisms are a categorical generalization of injective functions; in some categories the notions coincide, but monomorphisms are more general, as in the examples below. The categorical dual of a monomorphism is an epimorphism, i.e. a monomorphism in a category C is an epimorphism in the dual category Cop. Every section is a monomorphism, and every retraction is an epimorphism.
Definition of monomorphism in the English dictionary
The first definition of monomorphism in the dictionary is the fact of showing little or no change in structure during the entire life history. Other definition of monomorphism is the fact of existing or having parts that exist in only one form.Monomorphism is also the fact of having only one crystalline form.
The translations of monomorphism from English to other languages presented in this section have been obtained through automatic statistical translation; where the essential translation unit is the word «monomorphism» in English.
List of principal searches undertaken by users to access our English online dictionary and most widely used expressions with the word «monomorphism».
FREQUENCY OF USE OF THE TERM «MONOMORPHISM» OVER TIME
The graph expresses the annual evolution of the frequency of use of the word «monomorphism» during the past 500 years. Its implementation is based on analysing how often the term «monomorphism» appears in digitalised printed sources in English between the year 1500 and the present day.
Examples of use in the English literature, quotes and news about monomorphism
10 ENGLISH BOOKS RELATING TO «MONOMORPHISM»
Discover the use of monomorphism in the following bibliographical selection. Books relating to monomorphism and brief extracts from same to provide context of its use in English literature.
Real World Haskell: Code You Can Believe In
The Dreaded Monomorphism Restriction The Haskell 98 standard has a subtle
feature that can sometimes bite us in unexpected circumstances. Here's a simple
function definition that illustrates the issue: -- file: ch06/Monomorphism.hs ...
Bryan O'Sullivan, John Goerzen, Donald Bruce Stewart, 2008
Handbook of Game Theory with Economic Applications
[Cl Cl The proof of 14 reveals additional stability properties of a monomorphism
whose phenotype is an ESS p. Consider a specification (G, U, U,,) of (23) and let
U be the monomorphism of genotype p. We say that a population state c is nearer
Robert J. Aumann, Sergiu Hart, 1994
Lectures and Exercises on Functional Analysis
The following definition distinguishes just the "good" ones. Definition 2. A
morphism <p : X — > Y in 1C is called a monomorphism if <pi[>i = <pfa always
implies ipi = ip2. A morphism is called an epimorphism if it is a monomorphism in
the dual ...
Александр Яковлевич Хелемский
Canadian Mathematical Bulletin
A map in a category is called a regular monomorphism if it is the equalizer of a
pair of maps. If its cokernel pair exists, it is the equalizer of them. A map is called
a universal regular monomorphism if its pushout with every map with the same ...
Encyclopaedia of Mathematics
Kernel of a morphism in a category) is a normal monomorphism. The converse is
not true, in general; however, if cokernels (cf. Cokemel) of morphisms exist in &,
then every normal monomorphism turns out to be the kernel of its cokemel.
Michiel Hazewinkel, 1990
Categories of Modules Over Endomorphism Rings
Proof: (a) Assume j is an A-monomorphism in (Va)0, and choose a monomor-
phism j in M0(Va) such that qa(j) = j. By 4.2.4 i — ha(j) is a monomorphism in (Ta)
0 such that ta(i) = J, and by 3.1.10 T^ = q^, so that j = cut^i) = Ta(i). Conversely ...
Theodore G. Faticoni, 1993
An Introduction to Abstract Algebra
Monomorphisms A homomorphism that is 1-1 is known as a monomorphism.
Thus in a monomorphism different objects always have different images: in other
words gd = g'd => g = g'. The simplest way of testing for monomorphisms is by ...
Frederick Michael Hall, 1966
Categories and Sheaves
(a) u : A — » B is a local monomorphism. (b) for any diagram U =1 A — F B with
U S C such that the two compositions coincide, there exists a local epimorphism
S U such that the two compositions S U =1 A coincide, (c) for any diagram Z =4 A
Masaki Kashiwara, Pierre Schapira, 2006
Monomorphism. The sexes are similar in many monogamous species, for a
number of possible reasons. One is that sexual selection is so weak compared to
counteracting natural selection that no secondary sex differences have evolved.
M. B. Andersson, 1994
A morphism to which is an epimorphism, monomorphism or isomorphism of the
space K' into the space K", as defined in Sec. 2.71, is called an epimorphism,
monomorphism or isomorphism of the algebra K' into the algebra K", provided ...
Georgiĭ Evgenʹevich Shilov, 1977
3 NEWS ITEMS WHICH INCLUDE THE TERM «MONOMORPHISM»
Find out what the national and international press are talking about and how the term monomorphism is used in the context of the following news items.
Conservatism and novelty in the genetic architecture of adaptation in …
The heterogeneity in selection regimes shaping Heliconius wing patterns, that is, local monomorphism under directional selection versus ... «Nature.com, Mar 15»
Staub, science and salamanders
She studies the evolution of sexual dimorphism and monomorphism in various salamander species. Staub researches how salamanders send ... «Bulletin, Feb 15»
Ornithologists Map Family Tree of Mysterious Cotinga Birds
... while females are placed more interior; sexual monomorphism is indicated by the presence of only a single illustration at a given terminal; ... «Sci-News.com, Oct 14»
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