adjoint

Speech parts

1. adjoint - Noun

2. adjoint - Adjective

Meaning

An adjunct; a helper.

Synonyms

Phrases with the word

Examples

Additionally, every pair of adjoint functors comes equipped with two natural transformations (generally not isomorphisms) called the unit and counit. Source: Internet

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. Source: Internet

A particular case of this happens when a continuous functor admits a left adjoint. Source: Internet

Alternatively one can observe that the functor that for each group takes the underlying monoid (ignoring inverses) has a left adjoint. Source: Internet

An important property of adjoint functors is that every right adjoint functor is continuous and every left adjoint functor is cocontinuous. 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

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