adjunction

Noun

Meaning

The act of joining; the thing joined or added.

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Antonyms

Hypernyms

Examples

Adjunctions in full There are hence numerous functors and natural transformations associated with every adjunction, and only a small portion is sufficient to determine the rest. Source: Internet

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. Source: Internet

A similar argument allows one to construct a hom-set adjunction from the terminal morphisms to a left adjoint functor. Source: Internet

Equivalences of categories If a functor F: C←D is one half of an equivalence of categories then it is the left adjoint in an adjoint equivalence of categories, i.e. an adjunction whose unit and counit are isomorphisms. Source: Internet

It is probably wrong to say that he promoted the adjoint functor concept in isolation: but recognition of the role of adjunction was inherent in Grothendieck's approach. Source: Internet

One can verify directly that this correspondence is a natural transformation, which means it is a hom-set adjunction for the pair (F,G). Source: Internet

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