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Monoids is an English word. Below you'll find 10+ example sentences showing how it's used in practice.

Rare word

Monoids in a sentence

Related words

Monoids | Monoid

Monoids meaning

plural of monoid

Using Monoids

  • The main meaning on this page is: plural of monoid
  • In the example corpus, monoids often appears in combinations such as: monoids are, monoids and, of monoids.

Context around Monoids

  • Average sentence length in these examples: 19.4 words
  • Position in the sentence: 7 start, 4 middle, 2 end
  • Sentence types: 13 statements, 0 questions, 0 exclamations

Often before:

generalize 1× commutative 1× consequently 1× two 1×

Often after:

see 1× may 1× states 1×

Sentence patterns with Monoids

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

actions of monoids on sets 1× categories generalize monoids in the 1× commutative monoids are often 1× consequently monoids are studied 1× groups or monoids 1× homomorphism of monoids and is 1× monoids just like 1× objects are monoids and whose 1×

Sentence openings and endings

Common sentence openings:

as categories generalize 1× commutative monoids are 1× consequently monoids are 1× every completely multiplicative 1× many definitions and 1× monoids just like 1×

Common sentence endings:

a separate requirement 1× are monoid homomorphisms 1× axioms as above 1× but lacks identities 1× generalized for categories 1× groups or monoids 1×

Words around Monoids

Just before it in the word index:

monoidal 5 monoid 47 monohydrate 4 monohulls 7 monohull 13 monographs 28

Just after it in the word index:

monoikos 2 monoisotopic 3 monokaryons 4 monokini 3 monokle 5 monokoane 2

Similar in corpus frequency:

aanand 16 abcd 16 abdurrahman 16 aberdour 16 abergele 16 abg 16

Corpus analysis for Monoids

  • In this selection, "monoids" usually appears near the start of the sentence. The average example has 19.4 words, and this corpus slice is mostly made up of statements.
  • Around the word, generalize, commutative, consequently, see, may and states stand out and add context to how "monoids" is used.
  • Recognizable usage signals include actions of monoids on sets and categories generalize monoids in the. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "monoids" sits close to words such as aanand, abcd and abdurrahman, which helps place it inside the broader word index.

Example types with monoids

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

Commutative monoids are often written additively. (6 words)

Several definitions and theorems about monoids may be generalized for categories. (11 words)

For more on the relationship between category theory and monoids see below. (12 words)

Longer example sentences

More precisely: if A is an abelian group and we denote by m the group multiplication of A, by e the inclusion of the identity element, and by inv the inversion operation on A, then (A,m,e,inv) is a group object in the category of groups (or monoids). (50 words)

The first isomorphism theorem for monoids states that this quotient monoid is naturally isomorphic to the image of f (which is a submonoid of N),(for the congruence relation). (29 words)

Monoids, just like other algebraic structures, also form their own category, Mon, whose objects are monoids and whose morphisms are monoid homomorphisms. (22 words)

Example sentences (13)

Monoids, just like other algebraic structures, also form their own category, Mon, whose objects are monoids and whose morphisms are monoid homomorphisms.

As categories generalize monoids in the same way, a semigroupoid behaves much like a category but lacks identities.

Commutative monoids are often written additively.

Consequently, monoids are studied in the theory of semigroups rather than in group theory.

Every completely multiplicative function is a homomorphism of monoids and is completely determined by its restriction to the prime numbers.

For more on the relationship between category theory and monoids see below.

Many definitions and theorems about monoids can be generalised to small categories with more than one object.

More precisely: if A is an abelian group and we denote by m the group multiplication of A, by e the inclusion of the identity element, and by inv the inversion operation on A, then (A,m,e,inv) is a group object in the category of groups (or monoids).

Advertentie

Several definitions and theorems about monoids may be generalized for categories.

Since for monoids this isn't always true, it is necessary to state this as a separate requirement.

The first isomorphism theorem for monoids states that this quotient monoid is naturally isomorphic to the image of f (which is a submonoid of N),(for the congruence relation).

Two monoids are said to be isomorphic if there is a monoid isomorphism between them.

Variants and generalizations One can also consider actions of monoids on sets, by using the same two axioms as above.

Advertentie

Common combinations with monoids

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "monoids" in a sentence?
An example: "Monoids, just like other algebraic structures, also form their own category, Mon, whose objects are monoids and whose morphisms are monoid homomorphisms." This page contains 10+ example sentences with the word "monoids" from authentic English texts.
What does "monoids" mean?
Monoids means: plural of monoid
How many example sentences with "monoids" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "monoids", drawn from a database of millions of English sentences.