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How do you use Cohomology in a sentence? See 10+ example sentences showing how this word appears in different contexts, plus the exact meaning.

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Cohomology in a sentence

Cohomology meaning

  1. A method of contravariantly associating a family of invariant quotient groups to each algebraic or geometric object of a category, including categories of geometric and algebraic objects.
  2. A system of quotient groups associated to a topological space.

Using Cohomology

  • The main meaning on this page is: A method of contravariantly associating a family of invariant quotient groups to each algebraic or geometric object of a category, including categories of geometric and algebraic objects. | A system of quotient groups associated to a topological space.
  • In the example corpus, cohomology often appears in combinations such as: rham cohomology, cohomology theory, cohomology group.

Context around Cohomology

  • Average sentence length in these examples: 20.9 words
  • Position in the sentence: 2 start, 4 middle, 4 end
  • Sentence types: 10 statements, 0 questions, 0 exclamations

Often before:

rham 3× ordinary 2× generalized 1× weil 1× singular 1× real 1× using 1×

Often after:

theory 3× group 2× proof 1× arises 1×

Sentence patterns with Cohomology

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

cohomology arises from 1× de rham cohomology 1× de rham cohomology group h 1× de rham cohomology to singular 1× homology and cohomology as functors 1× in the cohomology proof 1× its generalized cohomology theory 1× or rather cohomology because the 1×

Sentence openings and endings

Common sentence openings:

cohomology arises from 1× de rham showed 1× michael atiyah and 1× several results showed 1× the proof using 1× the topological condition 1×

Common sentence endings:

certain axioms e 1× construction of homology 1× de rham cohomology 1× generalized cohomology theory 1× group is trivial 1× ordinary cohomology theory 1×

Words around Cohomology

Just before it in the word index:

cohome 2 cohoes 8 cohocton 7 coho 31 cohn 170 cohle 11

Just after it in the word index:

cohon 8 cohoon 3 cohort 412 cohorted 2 cohorting 4 cohorts 169

Similar in corpus frequency:

aanholt 13 aardwolf 13 abati 13 abbeville 13 abcc 13 abcon 13

Corpus analysis for Cohomology

  • In this selection, "cohomology" usually appears in the middle of the sentence. The average example has 20.9 words, and this corpus slice is mostly made up of statements.
  • Around the word, rham, ordinary, generalized, theory, group and proof stand out and add context to how "cohomology" is used.
  • Recognizable usage signals include cohomology arises from and de rham cohomology. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "cohomology" sits close to words such as aanholt, aardwolf and abati, which helps place it inside the broader word index.

Example types with cohomology

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

This gives a homomorphism from de Rham cohomology to singular cohomology. (11 words)

Cohomology arises from the algebraic dualization of the construction of homology. (11 words)

The topological condition is again that the second real cohomology group is trivial. (13 words)

Longer example sentences

The proof using Stokes's theorem is closely related to the proof using homology (or rather cohomology), because the form ω generates the de Rham cohomology group H n−1 (∂B) used in the cohomology proof. (36 words)

De Rham showed that all of these approaches were interrelated and that, for a closed, oriented manifold, the Betti numbers derived through simplicial homology were the same Betti numbers as those derived through de Rham cohomology. (36 words)

Michael Atiyah and Friedrich Hirzebruch (right), the creators of topological K-theory The Atiyah–Hirzebruch spectral sequence relates the ordinary cohomology of a space to its generalized cohomology theory. (29 words)

Example sentences (10)

The proof using Stokes's theorem is closely related to the proof using homology (or rather cohomology), because the form ω generates the de Rham cohomology group H n−1 (∂B) used in the cohomology proof.

Michael Atiyah and Friedrich Hirzebruch (right), the creators of topological K-theory The Atiyah–Hirzebruch spectral sequence relates the ordinary cohomology of a space to its generalized cohomology theory.

This cohomology theory was known as the "Weil cohomology", but using the tools he had available, Weil was unable to construct it.

This gives a homomorphism from de Rham cohomology to singular cohomology.

Cohomology arises from the algebraic dualization of the construction of homology.

De Rham showed that all of these approaches were interrelated and that, for a closed, oriented manifold, the Betti numbers derived through simplicial homology were the same Betti numbers as those derived through de Rham cohomology.

Several results showed that the newly introduced K-theory was in some ways more powerful than ordinary cohomology theory.

The topological condition is again that the second real cohomology group is trivial.

They defined homology and cohomology as functors equipped with natural transformations subject to certain axioms (e.

This paper shows how to convert from the K-theory version to a version using cohomology.

Common combinations with cohomology

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "cohomology" in a sentence?
An example: "The proof using Stokes's theorem is closely related to the proof using homology (or rather cohomology), because the form ω generates the de Rham cohomology group H n−1 (∂B) used in the cohomology proof." This page contains 10+ example sentences with the word "cohomology" from authentic English texts.
What does "cohomology" mean?
Cohomology means: A method of contravariantly associating a family of invariant quotient groups to each algebraic or geometric object of a category, including categories of geometric and algebraic objects.
How many example sentences with "cohomology" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "cohomology", drawn from a database of millions of English sentences.