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Wondering how to use Functors in a sentence? Below are 10+ example sentences from authentic English texts. Including the meaning .

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Functors in a sentence

Related words

Functors | Functor

Functors meaning

plural of functor

Using Functors

  • The main meaning on this page is: plural of functor
  • In the example corpus, functors often appears in combinations such as: adjoint functors, functors between, functors are.

Context around Functors

  • Average sentence length in these examples: 20.2 words
  • Position in the sentence: 13 start, 7 middle, 0 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Often before:

adjoint 7× free 2× cocontinuous 2× additive 2× forgetful 1× main 1× valued 1× ordinary 1× covariant 1× numerous 1×

Often after:

main 1× contravariant 1× defined 1× exist 1× comes 1× arise 1×

Sentence patterns with Functors

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

additive functors between preadditive 1× additive functors if c 1× adjoint functors arise everywhere 1× and cocontinuous functors 1× and cocontinuous functors there are 1× are free functors 1× between two functors is a 1× called covariant functors in order 1×

Sentence openings and endings

Common sentence openings:

a pair of 1× additionally every pair 1× additive functors between 1× additive functors if 1× adjoint functors arise 1× adjunctions in full 1×

Common sentence endings:

and cocontinuous functors 1× antitone galois connection 1× are free functors 1× are left adjoints 1× areas of mathematics 1× categories are functors 1×

Words around Functors

Just before it in the word index:

functorial 4 functor 88 functions 3.786 functionless 2 functionings 2 functioning 1.092

Just after it in the word index:

fund 10.996 funda 8 fundable 2 fundament 7 fundamenta 7 fundamental 2.714

Similar in corpus frequency:

abner 72 acquit 72 adamantly 72 allahabad 72 amon 72 anathema 72

Corpus analysis for Functors

  • In this selection, "functors" usually appears near the start of the sentence. The average example has 20.2 words, and this corpus slice is mostly made up of statements.
  • Around the word, adjoint, free, cocontinuous, main, contravariant and defined stand out and add context to how "functors" is used.
  • Recognizable usage signals include additive functors between preadditive and additive functors if c. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "functors" sits close to words such as abner, acquit and adamantly, which helps place it inside the broader word index.

Example types with functors

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

Functors main Functors are structure-preserving maps between categories. (9 words)

Adjoint functors arise everywhere, in all areas of mathematics. (9 words)

All higher Tor functors are assembled in the derived tensor product. (11 words)

Longer example sentences

Additive functors between preadditive categories generalize the concept of ring homomorphism, and ideals in additive categories can be defined as sets of morphisms closed under addition and under composition with arbitrary morphisms. (32 words)

By studying categories and functors, we are not just studying a class of mathematical structures and the morphisms between them; we are studying the relationships between various classes of mathematical structures. (31 words)

Definition If F and G are functors between the categories C and D, then a natural transformation η from F to G is a family of morphisms that satisfy two requirements. (31 words)

Example sentences (20)

Free functors: Going in the opposite direction of forgetful functors are free functors.

Continuous and cocontinuous functors There are two natural types of functors between sites.

Functors main Functors are structure-preserving maps between categories.

In fact, what we have done is define a category of categories and functors – the objects are categories, and the morphisms (between categories) are functors.

It allows the embedding of any category into a category of functors (contravariant set-valued functors) defined on that category.

Let F and G be a pair of adjoint functors with unit η and co-unit ε (see the article on adjoint functors for the definitions).

Ordinary functors are also called covariant functors in order to distinguish them from contravariant ones.

Since adjoint functors exist in abundance, this gives numerous examples of continuous and cocontinuous functors.

Advertentie

Additionally, every pair of adjoint functors comes equipped with two natural transformations (generally not isomorphisms) called the unit and counit.

Additive functors between preadditive categories generalize the concept of ring homomorphism, and ideals in additive categories can be defined as sets of morphisms closed under addition and under composition with arbitrary morphisms.

Additive functors If C and D are preadditive categories, then a functor F: C → D is additive if it too is enriched over the category Ab.

Adjoint functors arise everywhere, in all areas of mathematics.

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.

All higher Tor functors are assembled in the derived tensor product.

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

An arrow between two functors is a natural transformation when it is subject to certain naturality or commutativity conditions.

An important property of adjoint functors is that every right adjoint functor is continuous and every left adjoint functor is cocontinuous.

A pair of adjoint functors between two partially ordered sets is called a Galois connection (or, if it is contravariant, an antitone Galois connection).

By studying categories and functors, we are not just studying a class of mathematical structures and the morphisms between them; we are studying the relationships between various classes of mathematical structures.

Definition If F and G are functors between the categories C and D, then a natural transformation η from F to G is a family of morphisms that satisfy two requirements.

Advertentie

Common combinations with functors

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "functors" in a sentence?
An example: "Free functors: Going in the opposite direction of forgetful functors are free functors." This page contains 10+ example sentences with the word "functors" from authentic English texts.
What does "functors" mean?
Functors means: plural of functor
How many example sentences with "functors" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "functors", drawn from a database of millions of English sentences.