relationship are known as adjoint functors, one being the left adjoint and the other the right adjoint. Pairs of adjoint functors are ubiquitous in mathematics...

Look up adjoint in Wiktionary, the free dictionary. In mathematics, the term adjoint applies in several situations. Several of these share a similar formalism:...

colimits, like the strongly related notions of universal properties and adjoint functors, exist at a high level of abstraction. In order to understand them...

to the defining properties of pairs of adjoint functors in category theory, and this is where adjoint functors got their name from. Mathematical concepts...

pairs of adjoint functors. Functors sometimes appear in functional programming. For instance, the programming language Haskell has a class Functor where...

concept of adjoint functors was introduced independently by Daniel Kan in 1958. Mathematics portal Free object Natural transformation Adjoint functor Monad...

are functors adjoint to each other, then T = G ∘ F {\displaystyle T=G\circ F} together with η , μ {\displaystyle \eta ,\mu } determined by the adjoint relation...

a branch of mathematics, a functor category D C {\displaystyle D^{C}} is a category where the objects are the functors F : C → D {\displaystyle F:C\to...

: X → Y {\displaystyle u:X\to Y} is a pair of adjoint functors (u∗,u∗) (where u∗ : Y → X is left adjoint to u∗ : X → Y) such that u∗ preserves finite limits...

of a forgetful functor with no adjoint. There is no field satisfying a free universal property for a given set. Adjoint functors Functors Projection (set...