1. adjoint - Noun
2. adjoint - Adjective
An adjunct; a helper.
Source: Webster's dictionaryAdditionally, 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