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Explore Cokernel through 8 example sentences from English, with an explanation of the meaning. Ideal for language learners, writers and word enthusiasts.

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Cokernel in a sentence

Related words

Cokernel | Cokernels

Cokernel meaning

  1. The coequalizer of f and the zero morphism from X to Y, denoted operatorname cokerf.
  2. The target of operatorname cokerf, denoted operatorname Cokerf.

Using Cokernel

  • The main meaning on this page is: The coequalizer of f and the zero morphism from X to Y, denoted operatorname cokerf. | The coequalizer of f and the zero morphism from X to Y, denoted operatorname cokerf. | The target of operatorname cokerf, denoted operatorname Cokerf.
  • In the example corpus, cokernel often appears in combinations such as: cokernel of, the cokernel, and cokernel.

Context around Cokernel

  • Average sentence length in these examples: 20.4 words
  • Position in the sentence: 0 start, 4 middle, 4 end
  • Sentence types: 8 statements, 0 questions, 0 exclamations

Often after:

functors 1×

Sentence patterns with Cokernel

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

and a cokernel 1× construction the cokernel of ƒ 1× is a cokernel of some 1× kernel and cokernel make sense 1× kernel and cokernel of f 1× that every cokernel is an 1× that the cokernel functors for 1× while the cokernel of f 1×

Sentence openings and endings

Common sentence openings:

analogously one can 1× it follows in 1× kernels and cokernels 1× specifically ab1 every 1× this means that 1× unlike with products 1×

Common sentence endings:

a preadditive category 1× a suitable category 1× and a cokernel 1× are left adjoints 1× cokernel make sense 1× is an epimorphism 1×

Words around Cokernel

Just before it in the word index:

coker 71 coked 4 coke 296 cokayne 2 cokato 5 cokanasiga 6

Just after it in the word index:

cokernels 3 cokes 16 cokey 2 coki 2 cokie 8 coking 24

Similar in corpus frequency:

aargau 11 abacos 11 abboud 11 abbreviate 11 abdelkader 11 abdomens 11

Corpus analysis for Cokernel

  • In this selection, "cokernel" usually appears in the middle of the sentence. The average example has 20.4 words, and this corpus slice is mostly made up of statements.
  • Around the word, functors stand out and add context to how "cokernel" is used.
  • Recognizable usage signals include and a cokernel and construction the cokernel of ƒ. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "cokernel" sits close to words such as aargau, abacos and abboud, which helps place it inside the broader word index.

Example types with cokernel

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

It follows in particular that every cokernel is an epimorphism. (10 words)

Specifically: * AB1) Every morphism has a kernel and a cokernel. (10 words)

Analogously, one can show that the cokernel functors for abelian groups, vector spaces and modules are left adjoints. (18 words)

Longer example sentences

That is, if f: A → B is a morphism in a preadditive category, then the kernel of f is the equaliser of f and the zero morphism from A to B, while the cokernel of f is the coequaliser of f and this zero morphism. (45 words)

Kernels and cokernels Because the hom-sets in a preadditive category have zero morphisms, the notion of kernel and cokernel make sense. (22 words)

This means that every monomorphism is a kernel of some morphism, and every epimorphism is a cokernel of some morphism. (20 words)

Example sentences (8)

Analogously, one can show that the cokernel functors for abelian groups, vector spaces and modules are left adjoints.

It follows in particular that every cokernel is an epimorphism.

Kernels and cokernels Because the hom-sets in a preadditive category have zero morphisms, the notion of kernel and cokernel make sense.

Specifically: * AB1) Every morphism has a kernel and a cokernel.

That is, if f: A → B is a morphism in a preadditive category, then the kernel of f is the equaliser of f and the zero morphism from A to B, while the cokernel of f is the coequaliser of f and this zero morphism.

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

Unlike with products and coproducts, the kernel and cokernel of f are generally not equal in a preadditive category.

With an analogous construction, the cokernel of ƒ can be seen as an initial object of a suitable category.

Common combinations with cokernel

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "cokernel" in a sentence?
An example: "Analogously, one can show that the cokernel functors for abelian groups, vector spaces and modules are left adjoints." This page contains 8 example sentences with the word "cokernel" from authentic English texts.
What does "cokernel" mean?
Cokernel means: The coequalizer of f and the zero morphism from X to Y, denoted operatorname cokerf.
How many example sentences with "cokernel" are there?
Voorbeeldzinnen.info contains 8 example sentences with "cokernel", drawn from a database of millions of English sentences.