Examples of 'functor' in a sentence
Meaning of "functor"
functor (noun): In mathematics, a functor is a mapping between categories that preserves the relationships between objects and morphisms
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- A function word.
- A function object.
- A category homomorphism; a morphism from a source category to a target category which maps objects to objects and arrows to arrows, in such a way as to preserve domains and codomains (of the arrows) as well as composition and identities.
- A structure allowing a function to apply within a generic type, in a way that is conceptually similar to a functor in category theory.
How to use "functor" in a sentence
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functor
A multifunctor is a generalization of the functor concept to n variables.
Identity of composition of functors is the identity functor.
A functor with a left and a right adjoint.
Another common work around is using a functor.
The functor is in the two categories.
This makes the construction into a functor.
A functor is a homomorphism between two categories.
An embedding can also refer to an embedding functor.
A particularly common type of functor is the predicate.
Any functor which is part of an equivalence is essentially surjective.
This behavior is described in the functor laws.
A functor whose domain is a product category is known as a bifunctor.
I have now a better understanding of what a functor is.
It can be seen as a functor in two arguments.
I think that what you described is a functor.
See also
Every faithful functor from a balanced category is conservative.
It uses the exact functor theorem.
This functor is the derived functor of the functor HomRM.
Then the fact is that the functor is an equivalence.
A formal group is usually defined as a particular kind of a group functor.
The forgetful functor from semigroups to sets is monadic.
This allows the entire chain complex to be treated as a functor.
The arity of a functor is the number of arguments it takes.
Every flat resolution is acyclic with respect to this functor.
The second functor is also a presheaf.
Full and faithful functor.
The identity functor is an endofunctor.
Where the coefficients are given by the covariant functor.
Conservative functor in nLab.
A functor from spaces to spectra fulfilling these properties is called excisive.
An important goal in many settings is to determine whether a given functor is representable.
A strict monoidal functor is a monoidal functor whose coherence maps are identities.
Freyd is perhaps best known for his adjoint functor theorem.
A functor to the comma category selects that particular collection of morphisms.
A list comprehension is a list whose first element has the functor.
A functor is a generalization on a function.
Right derived functor.
A functor is exact if and only if it is both left exact and right exact.
Fully faithful functor.
This functor is left adjoint to the forgetful functor from groups to sets.
Canonical projection functor.
An enriched functor is the appropriate generalization of the notion of a functor to enriched categories.
Internal hom functor.
Functor of points.
There is a canonical functor.
The axioms for a functor require that these play harmoniously with substitution.
Thus we have a functor.
This functor has a left adjoint which is the integral group ring construction.
And there is a functor.
This is a left exact functor and thus has right derived functors RnT.
