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On this page you'll find 8 example sentences with Colimit. Discover the meaning, how to use the word correctly in a sentence.

Rare word

Colimit in a sentence

Related words

Colimit | Colimits

Colimit meaning

The dual of a limit; the cocone of a diagram through which any other cocone of that same diagram can factor uniquely.

Using Colimit

  • The main meaning on this page is: The dual of a limit; the cocone of a diagram through which any other cocone of that same diagram can factor uniquely.
  • In the example corpus, colimit often appears in combinations such as: has colimit, colimit in, colimit functor.

Context around Colimit

  • Average sentence length in these examples: 30.9 words
  • Position in the sentence: 2 start, 6 middle, 0 end
  • Sentence types: 8 statements, 0 questions, 0 exclamations

Often after:

functor 2× object 1× provides 1×

Sentence patterns with Colimit

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

has a colimit in c 3× any colimit functor is 1× diagram its colimit 1× exists a colimit functor which 1× has a colimit then this 1× into the colimit object 1× is a colimit of the 1× limit and colimit provides an 1×

Sentence openings and endings

Common sentence openings:

a category has 1× any colimit functor 1× dually an initial 1× dually if a 1× dually if every 1× more examples every 1×

Common sentence endings:

a unique isomorphism 1× a universal cone 1× all small colimits 1× diagram its colimit 1× functor as domain 1× or categorical sum 1×

Words around Colimit

Just before it in the word index:

colima 7 colijn 2 colihan 2 coligny 9 coliform 12 colie 3

Just after it in the word index:

colimits 17 colin 1.121 colina 11 colinas 8 colindale 3 colindres 2

Similar in corpus frequency:

aargau 11 abacos 11 abboud 11 abbreviate 11 abdelkader 11 abdomens 11

Corpus analysis for Colimit

  • In this selection, "colimit" usually appears in the middle of the sentence. The average example has 30.9 words, and this corpus slice is mostly made up of statements.
  • Around the word, functor, object and provides stand out and add context to how "colimit" is used.
  • Recognizable usage signals include has a colimit in c and any colimit functor is. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "colimit" sits close to words such as aargau, abacos and abboud, which helps place it inside the broader word index.

Example types with colimit

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

Dually, an initial object is a colimit of the empty diagram ∅ → C and can be thought of as an empty coproduct or categorical sum. (24 words)

Dually, if every diagram of type J has a colimit in C (for J small) there exists a colimit functor : which assigns each diagram its colimit. (26 words)

A category has colimits of type J if every diagram of type J has a colimit in C. A cocomplete category is one that has all small colimits. (28 words)

Longer example sentences

Properties Existence of limits A given diagram F : J → C may or may not have a limit (or colimit) in C. Indeed, there may not even be a cone to F, let alone a universal cone. (36 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)

They can be characterized as initial objects in the category of co-cones from F. As with limits, if a diagram F has a colimit then this colimit is unique up to a unique isomorphism. (35 words)

Example sentences (8)

Dually, if every diagram of type J has a colimit in C (for J small) there exists a colimit functor : which assigns each diagram its colimit.

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.

They can be characterized as initial objects in the category of co-cones from F. As with limits, if a diagram F has a colimit then this colimit is unique up to a unique isomorphism.

A category has colimits of type J if every diagram of type J has a colimit in C. A cocomplete category is one that has all small colimits.

Dually, an initial object is a colimit of the empty diagram ∅ → C and can be thought of as an empty coproduct or categorical sum.

Dually, if a diagram F : J → C has a colimit in C, denoted colim F, there is a unique canonical isomorphism : which is natural in the variable N and respects the colimiting cones.

More examples Every limit and colimit provides an example for a simple natural transformation, as a cone (category theory) amounts to a natural transformation with the diagonal functor as domain.

Properties Existence of limits A given diagram F : J → C may or may not have a limit (or colimit) in C. Indeed, there may not even be a cone to F, let alone a universal cone.

Common combinations with colimit

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "colimit" in a sentence?
An example: "Dually, if every diagram of type J has a colimit in C (for J small) there exists a colimit functor : which assigns each diagram its colimit." This page contains 8 example sentences with the word "colimit" from authentic English texts.
What does "colimit" mean?
Colimit means: The dual of a limit; the cocone of a diagram through which any other cocone of that same diagram can factor uniquely.
How many example sentences with "colimit" are there?
Voorbeeldzinnen.info contains 8 example sentences with "colimit", drawn from a database of millions of English sentences.