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

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Groupoid in a sentence

Related words

Groupoid | Groupoids

Groupoid meaning

  1. A magma: a set with a total binary operation.
  2. A set with a partial binary operation that is associative and has identities and inverses.

Using Groupoid

  • The main meaning on this page is: A magma: a set with a total binary operation. | A set with a partial binary operation that is associative and has identities and inverses.
  • In the example corpus, groupoid often appears in combinations such as: groupoid is, fundamental groupoid, groupoid of.

Context around Groupoid

  • Average sentence length in these examples: 19.7 words
  • Position in the sentence: 7 start, 6 middle, 4 end
  • Sentence types: 17 statements, 0 questions, 0 exclamations

Often before:

fundamental 3× linear 2× action 2× free 1× full 1×

Often after:

include 1× comes 1× instead 1×

Sentence patterns with Groupoid

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

a free groupoid on a 1× a groupoid can be 1× a groupoid is a 1× general linear groupoid gl k 1× general linear groupoid is both 1× given a groupoid in the 1× have a groupoid in the 1× itself a groupoid 1×

Sentence openings and endings

Common sentence openings:

a groupoid can 1× a groupoid is 1× category of groupoids 1× examples linear algebra 1× further the stabilizers 1× given a groupoid 1×

Common sentence endings:

construction is functorial 1× directed graph does 1× group g x 1× is an isomorphism 1× itself a groupoid 1× just a group 1×

Words around Groupoid

Just before it in the word index:

groupme 9 groupm 7 groupings 160 grouping 329 groupies 11 groupie 15

Just after it in the word index:

groupoids 13 groupon 28 groups 15.638 groupthink 27 groupware 11 grousbeck 10

Similar in corpus frequency:

aav 21 abdicating 21 abductor 21 abet 21 abh 21 abhorred 21

Corpus analysis for Groupoid

  • In this selection, "groupoid" usually appears near the start of the sentence. The average example has 19.7 words, and this corpus slice is mostly made up of statements.
  • Around the word, fundamental, linear, action, include, comes and instead stand out and add context to how "groupoid" is used.
  • Recognizable usage signals include a free groupoid on a and a groupoid can be. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "groupoid" sits close to words such as aav, abdicating and abductor, which helps place it inside the broader word index.

Example types with groupoid

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

Thus we have a groupoid in the algebraic sense. (9 words)

This groupoid is called the fundamental groupoid of X, denoted (X). (11 words)

Thus any groupoid is equivalent to a multiset of unrelated groups. (11 words)

Longer example sentences

The advantages of regarding an equivalence relation as a special case of a groupoid include: *Whereas the notion of "free equivalence relation" does not exist, that of a free groupoid on a directed graph does. (35 words)

Given a groupoid in the category-theoretic sense, let G be the disjoint union of all of the sets G(x,y) (i.e. the sets of morphisms from x to y). (32 words)

Examples Linear algebra Given a field K, the corresponding general linear groupoid GL * (K) consists of all invertible matrices whose entries range over K. Matrix multiplication interprets composition. (28 words)

Example sentences (17)

The advantages of regarding an equivalence relation as a special case of a groupoid include: *Whereas the notion of "free equivalence relation" does not exist, that of a free groupoid on a directed graph does.

This groupoid is called the fundamental groupoid of X, denoted (X).

A groupoid can be seen as a: * Group with a partial function replacing the binary operation ; * Category in which every morphism is invertible.

A groupoid is a category in which every morphism is an isomorphism.

Category of groupoids A subgroupoid is a subcategory that is itself a groupoid.

Examples Linear algebra Given a field K, the corresponding general linear groupoid GL * (K) consists of all invertible matrices whose entries range over K. Matrix multiplication interprets composition.

Further the stabilizers of the action are the vertex groups, and the orbits of the action are the components, of the action groupoid.

Given a groupoid in the category-theoretic sense, let G be the disjoint union of all of the sets G(x,y) (i.e. the sets of morphisms from x to y).

Advertentie

If x is an object of the groupoid G, then the set of all morphisms from x to x forms a group G(x).

The general linear groupoid is both equivalent and isomorphic to the disjoint union of the various general linear groups GL n (F).

This action groupoid comes with a morphism which is a covering morphism of groupoids.

This occurs in topology because if a group G acts on a space X it also acts on the fundamental groupoid π 1 (X) of the space.

Thus any groupoid is equivalent to a multiset of unrelated groups.

Thus one has the fundamental groupoid instead of the fundamental group, and this construction is functorial.

Thus we have a groupoid in the algebraic sense.

Thus when groupoids arise in terms of other structures, as in the above examples, it can be helpful to maintain the full groupoid.

Using the algebraic definition, such a groupoid is literally just a group.

Advertentie

Common combinations with groupoid

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "groupoid" in a sentence?
An example: "The advantages of regarding an equivalence relation as a special case of a groupoid include: *Whereas the notion of "free equivalence relation" does not exist, that of a free groupoid on a directed graph does." This page contains 10+ example sentences with the word "groupoid" from authentic English texts.
What does "groupoid" mean?
Groupoid means: A magma: a set with a total binary operation.
How many example sentences with "groupoid" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "groupoid", drawn from a database of millions of English sentences.