Examples of using Functor in English and their translations into Italian
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Colloquial
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Official
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Medicine
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Financial
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Ecclesiastic
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Ecclesiastic
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Computer
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Programming
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Official/political
Dually, using that G is a functor, that η is natural, and the counit-unit equation 1GX G(εX)
Functors are structure-preserving maps between categories.
Categories and functors, module categories.
For details, see the article on hom functors.
categories, functors, natural transformations, universal properties.
These algebraic free functors have generally the same description as in the detailed description of the free group situation above.
If one starts looking for these adjoint pairs of functors, they turn out to be very common in abstract algebra, and elsewhere as well.
There are hence numerous functors and natural transformations associated with every adjunction,
These subcategories are precisely the kernels of exact functors from A to another abelian category.
The definition via counit-unit adjunction is convenient for proofs about functors which are known to be adjoint,
A suitable variation of this example also shows that the kernel functors for vector spaces
Analogously, one can show that the cokernel functors for abelian groups,
G-) as functors.
give rise to numerous adjoint pairs of functors.
In addition to class type functors, other kinds of function objects are also possible in C.
then the category of all additive functors from C to A also forms an abelian category.
then the category of all functors from C to A forms an abelian category.
adjunction is a relationship that two functors may have.
of sheaf cohomology on all topological spaces, as derived functors.
are the relevant functors between Abelian categories.