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Get to know Monomorphism better with 10+ real example sentences, the meaning.

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Monomorphism in a sentence

Related words

Monomorphism | Monomorphisms

Monomorphism meaning

  1. an injective homomorphism
  2. the absence of sexual dimorphism
  3. A morphism n such that for any other morphisms f and g, if n∘f=n∘g then f = g.

Using Monomorphism

  • The main meaning on this page is: an injective homomorphism | the absence of sexual dimorphism | A morphism n such that for any other morphisms f and g, if n∘f=n∘g then f = g.
  • In the example corpus, monomorphism often appears in combinations such as: monomorphism and, regular monomorphism, is monomorphism.

Context around Monomorphism

  • Average sentence length in these examples: 20.7 words
  • Position in the sentence: 3 start, 3 middle, 6 end
  • Sentence types: 12 statements, 0 questions, 0 exclamations

Often before:

regular 2× strong 1× extremal 1× terms 1× uses 1×

Often after:

strong 1× equalizes 1× kernels 1×

Sentence patterns with Monomorphism

These short patterns come directly from the example sentences and show how the word is often embedded:

by a monomorphism 2× a regular monomorphism equalizes some 1× and a monomorphism kernels are 1× and extremal monomorphism 1× both a monomorphism and an 1× bourbaki uses monomorphism as shorthand 1× companion terms monomorphism and epimorphism 1× involving a monomorphism 1×

Sentence openings and endings

Common sentence openings:

a regular monomorphism 1× a strong epimorphism 1× for instance since 1× in an abelian 1× in many categories 1× related concepts there 1×

Common sentence endings:

by a monomorphism 2× an injective function 1× and an epimorphism 1× and extremal monomorphism 1× in abelian categories 1× in this category 1×

Words around Monomorphism

Just before it in the word index:

monomorphic 2 monomino 3 monomial 2 monomers 32 monomeric 13 monomer 31

Just after it in the word index:

monomorphisms 6 monomotapa 3 monomoy 12 monomyth 6 monon 5 monona 12

Similar in corpus frequency:

aami 15 aat 15 abada 15 abcs 15 abdulkareem 15 abha 15

Corpus analysis for Monomorphism

  • In this selection, "monomorphism" usually appears near the end of the sentence. The average example has 20.7 words, and this corpus slice is mostly made up of statements.
  • Around the word, regular, strong, extremal, strong, equalizes and kernels stand out and add context to how "monomorphism" is used.
  • Recognizable usage signals include by a monomorphism and a regular monomorphism equalizes some. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "monomorphism" sits close to words such as aami, aat and abada, which helps place it inside the broader word index.

Example types with monomorphism

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

Every section is a monomorphism. (5 words)

A regular monomorphism equalizes some parallel pair of morphisms. (9 words)

Related concepts There are also useful concepts of regular monomorphism, strong monomorphism, and extremal monomorphism. (15 words)

Longer example sentences

For instance, since a function is bijective if and only if it is both injective and surjective, in abstract algebra a homomorphism is an isomorphism if and only if it is both a monomorphism and an epimorphism. (37 words)

This is represented in the diagram by an object and a monomorphism (kernels are always monomorphisms), which complete the short exact sequence running from the lower left to the upper right of the diagram. (34 words)

This epimorphism is called the coimage of f, while the monomorphism is called the image of f. Subobjects and quotient objects are well-behaved in abelian categories. (27 words)

Example sentences (12)

Related concepts There are also useful concepts of regular monomorphism, strong monomorphism, and extremal monomorphism.

Terminology The companion terms monomorphism and epimorphism were originally introduced by Nicolas Bourbaki ; Bourbaki uses monomorphism as shorthand for an injective function.

A regular monomorphism equalizes some parallel pair of morphisms.

A strong epimorphism satisfies a certain lifting property with respect to commutative squares involving a monomorphism.

Every section is a monomorphism.

For instance, since a function is bijective if and only if it is both injective and surjective, in abstract algebra a homomorphism is an isomorphism if and only if it is both a monomorphism and an epimorphism.

In an abelian category, every morphism f can be written as the composition of an epimorphism followed by a monomorphism.

In many categories it is possible to write every morphism as the composition of an epimorphism followed by a monomorphism.

Advertentie

This epimorphism is called the coimage of f, while the monomorphism is called the image of f. Subobjects and quotient objects are well-behaved in abelian categories.

This is not an injective map, as for example every integer is mapped to 0. Nevertheless, it is a monomorphism in this category.

This is represented in the diagram by an object and a monomorphism (kernels are always monomorphisms), which complete the short exact sequence running from the lower left to the upper right of the diagram.

This means that every monomorphism is a kernel of some morphism, and every epimorphism is a cokernel of some morphism.

Advertentie

Common combinations with monomorphism

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "monomorphism" in a sentence?
An example: "Related concepts There are also useful concepts of regular monomorphism, strong monomorphism, and extremal monomorphism." This page contains 10+ example sentences with the word "monomorphism" from authentic English texts.
What does "monomorphism" mean?
Monomorphism means: an injective homomorphism
How many example sentences with "monomorphism" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "monomorphism", drawn from a database of millions of English sentences.