Examples of using Functors in English and their translations into Dutch
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Colloquial
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Official
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Ecclesiastic
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Medicine
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Financial
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Computer
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Ecclesiastic
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Official/political
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Programming
Instances of such classes are called functors or function objects.
Contravariant functors are also occasionally called cofunctors.
Hence, a natural transformation can be considered to be a"morphism of functors.
Functors===The STL includes classes that overload the function call operator.
In the category of small categories, functors can be thought of more generally as morphisms.
Functors are important in all areas within mathematics to which category theory is applied.
homological algebra is the study of homological functors and the intricate algebraic structures that they entail.
Nowadays, functors are used throughout modern mathematics to relate various categories.
Limits and colimits, like the strongly related notions of universal properties and adjoint functors, exist at a high level of abstraction.
after categories and functors, one of the most fundamental notions of category theory
and the representations as functors from the object category to the category of vector spaces.
Functors were first considered in algebraic topology,
Saunders Mac Lane introduced categories, functors, and natural transformations as part of their work in topology,
Functors were first considered in algebraic topology,
functions by functors, and equations by natural isomorphisms of functors satisfying additional properties.
Additive functors between preadditive categories generalize the concept of ring homomorphism,
or the category of functors from a small category to an Abelian category are Abelian as well.
the morphisms are natural transformations between the functors.
He was recognised, in addition to his own research contributions such as work on signalizer functors, as a leader in directing the classification proof,
The functor is in the two categories.
The functor… Go on. is in the two categories.
The functor… is in the two categories.
In general, that forgetful functor is not full.
The limit of any functor from a discrete category into another category is called a product,
This functor is not full as there are functions between groups that are not group homomorphisms.
There is an inclusion functor: Set→ Med↪ Mag as trivial magmas,
If the signature is left as an empty list, the functor is simply to take the underlying set of a structure.
in general, that forgetful functor is not full.
the cone of a functor is an abstract notion used to define the limit of that functor. .
Functor categories are of interest for two main reasons:* many commonly occurring categories are(disguised) functor categories, so any statement proved for general functor categories is widely applicable;* every category embeds in a functor category(via the Yoneda embedding); the functor category often has nicer properties than the original category,