Bijections is an English word. Below you'll find 10+ example sentences showing how it's used in practice.
Bijections meaning
plural of bijection
Using Bijections
- The main meaning on this page is: plural of bijection
- In the example corpus, bijections often appears in combinations such as: bijections are, two bijections, the bijections.
Context around Bijections
- Average sentence length in these examples: 21.5 words
- Position in the sentence: 3 start, 4 middle, 4 end
- Sentence types: 11 statements, 0 questions, 0 exclamations
Corpus analysis for Bijections
- In this selection, "bijections" usually appears in the middle of the sentence. The average example has 21.5 words, and this corpus slice is mostly made up of statements.
- Around the word, two, theory and set stand out and add context to how "bijections" is used.
- Recognizable usage signals include as the bijections from s and bijections and category. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "bijections" sits close to words such as aadi, aayush and abbottabad, which helps place it inside the broader word index.
Example types with bijections
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
The inductive step follows directly from these two bijections. (9 words)
However, the bijections are not always the isomorphisms for more complex categories. (12 words)
Composition The composition of two bijections f: X → Y and g: Y → Z is a bijection. (16 words)
Additivity If C and D are preadditive categories and F : C ← D is an additive functor with a right adjoint G : C → D, then G is also an additive functor and the hom-set bijections : are, in fact, isomorphisms of abelian groups. (42 words)
The composition of any two elements of G exists, because the domain and codomain of any element of G is A. Moreover, the composition of bijections is bijective ; Wallace, D. A. R., 1998. (33 words)
The "active" way to regard permutations of a set S (finite or infinite) is to define them as the bijections from S to itself. (24 words)
Example sentences (11)
Bijections and category theory Bijections are precisely the isomorphisms in the category Set of sets and set functions.
Additivity If C and D are preadditive categories and F : C ← D is an additive functor with a right adjoint G : C → D, then G is also an additive functor and the hom-set bijections : are, in fact, isomorphisms of abelian groups.
Any Galois connection gives rise to closure operators and to inverse order-preserving bijections between the corresponding closed elements.
Composition The composition of two bijections f: X → Y and g: Y → Z is a bijection.
However, the bijections are not always the isomorphisms for more complex categories.
Moreover, the image of the map Diff(M) → Σ(π 0 (M)) is the bijections of π 0 (M) that preserve diffeomorphism classes.
Only bijections have two-sided inverses, but any function has a quasi-inverse, i.e. the full transformation monoid is regular.
Since the composition of two bijections always gives another bijection, the product of two permutations is again a permutation.
The "active" way to regard permutations of a set S (finite or infinite) is to define them as the bijections from S to itself.
The composition of any two elements of G exists, because the domain and codomain of any element of G is A. Moreover, the composition of bijections is bijective ; Wallace, D. A. R., 1998.
The inductive step follows directly from these two bijections.
Common combinations with bijections
These word pairs occur most frequently in English texts: