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Get to know Adjunction better with 10+ real example sentences, the meaning and synonyms like junction or joining.

Rare word

Adjunction in a sentence

Related words

Adjunction | Adjunctions

Adjunction meaning

  1. The act of joining; the thing joined or added.
  2. The joining of personal property owned by one to that owned by another.
  3. The process of adjoining elements to an algebraic structure (usually a ring or field); the result of such a process.

Synonyms of Adjunction

junction joining connection connexion

Related words

Other words often associated with Adjunction or its synonyms:

link instrumentation connectedness unification relation instrumentality connector union connective remembering articulation form

Using Adjunction

  • The main meaning on this page is: The act of joining; the thing joined or added. | The joining of personal property owned by one to that owned by another. | The process of adjoining elements to an algebraic structure (usually a ring or field); the result of such a process.
  • Useful related words include: junction, joining, connection, connexion.
  • In the example corpus, adjunction often appears in combinations such as: an adjunction, adjunction is, hom-set adjunction.

Context around Adjunction

  • Average sentence length in these examples: 27.3 words
  • Position in the sentence: 1 start, 4 middle, 5 end
  • Sentence types: 10 statements, 0 questions, 0 exclamations

Often before:

set 2× unit 1×

Often after:

provides 1×

Sentence patterns with Adjunction

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

adjunction is ubiquitous 1× constructing an adjunction that gives 1× counit unit adjunction is as 1× describes an adjunction between the 1× e an adjunction whose unit 1× hom set adjunction for the 1× hom set adjunction from the 1× of the adjunction provides the 1×

Sentence openings and endings

Common sentence openings:

a similar argument 1× adjunction is ubiquitous 1× adjunctions in full 1× any colimit functor 1× equivalences of categories 1× it is probably 1×

Common sentence endings:

a given monad 1× be the identity 1× counit are isomorphisms 1× determine the rest 1× grothendieck s approach 1× known as soberification 1×

Words around Adjunction

Just before it in the word index:

adjunct 178 adjumani 2 adjuged 2 adjudicatory 7 adjudicators 18 adjudicator 30

Just after it in the word index:

adjunctions 4 adjunctive 4 adjuncts 14 adjured 2 adjust 1.454 adjustability 9

Similar in corpus frequency:

aab 13 aamer 13 aave 13 abdelmadjid 13 abdulkarim 13 abdulsalami 13

Corpus analysis for Adjunction

  • In this selection, "adjunction" usually appears near the end of the sentence. The average example has 27.3 words, and this corpus slice is mostly made up of statements.
  • Around the word, set, unit and provides stand out and add context to how "adjunction" is used.
  • Recognizable usage signals include adjunction is ubiquitous and constructing an adjunction that gives. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "adjunction" sits close to words such as aab, aamer and aave, which helps place it inside the broader word index.

Example types with adjunction

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

Adjunction is ubiquitous in mathematics, as it specifies intuitive notions of optimization and efficiency. (14 words)

A similar argument allows one to construct a hom-set adjunction from the terminal morphisms to a left adjoint functor. (20 words)

One can verify directly that this correspondence is a natural transformation, which means it is a hom-set adjunction for the pair (F,G). (24 words)

Longer example sentences

Equivalences of categories If a functor F: C←D is one half of an equivalence of categories then it is the left adjoint in an adjoint equivalence of categories, i.e. an adjunction whose unit and counit are isomorphisms. (39 words)

Any colimit functor is left adjoint to a corresponding diagonal functor (provided the category has the type of colimits in question), and the unit of the adjunction provides the defining maps into the colimit object. (35 words)

Then, a direct verification that they form a counit-unit adjunction is as follows: The first counit-unit equation says that for each set Y the composition : should be the identity. (31 words)

Example sentences (10)

Adjunction is ubiquitous in mathematics, as it specifies intuitive notions of optimization and efficiency.

Adjunctions in full There are hence numerous functors and natural transformations associated with every adjunction, and only a small portion is sufficient to determine the rest.

Any colimit functor is left adjoint to a corresponding diagonal functor (provided the category has the type of colimits in question), and the unit of the adjunction provides the defining maps into the colimit object.

A similar argument allows one to construct a hom-set adjunction from the terminal morphisms to a left adjoint functor.

Equivalences of categories If a functor F: C←D is one half of an equivalence of categories then it is the left adjoint in an adjoint equivalence of categories, i.e. an adjunction whose unit and counit are isomorphisms.

It is probably wrong to say that he promoted the adjoint functor concept in isolation: but recognition of the role of adjunction was inherent in Grothendieck's approach.

One can verify directly that this correspondence is a natural transformation, which means it is a hom-set adjunction for the pair (F,G).

The article on Stone duality describes an adjunction between the category of topological spaces and the category of sober spaces that is known as soberification.

Then, a direct verification that they form a counit-unit adjunction is as follows: The first counit-unit equation says that for each set Y the composition : should be the identity.

Two constructions, called the category of Eilenberg–Moore algebras and the Kleisli category are two extremal solutions to the problem of constructing an adjunction that gives rise to a given monad.

Common combinations with adjunction

These word pairs occur most frequently in English texts:

  • an adjunction 3×
  • adjunction is 2×
  • hom-set adjunction 2×

Frequently asked questions

How do you use "adjunction" in a sentence?
An example: "Adjunction is ubiquitous in mathematics, as it specifies intuitive notions of optimization and efficiency." This page contains 10+ example sentences with the word "adjunction" from authentic English texts.
What does "adjunction" mean?
Adjunction means: The act of joining; the thing joined or added.
What are synonyms of "adjunction"?
Common synonyms of "adjunction" include: junction, joining, connection, connexion.
How many example sentences with "adjunction" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "adjunction", drawn from a database of millions of English sentences.