Adjoint functors - Wikipedia In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories Two functors that stand in this relationship are known as adjoint functors, one being the left adjoint and the other the right adjoint
adjunction in nLab A pair of 1-morphisms in a 2-category form an adjunction if they are dual to each other (Lambek (1982), cf here) in a precise sense There are two archetypical classes of examples:
What is an Adjunction? Part 3 (Examples) - Math3ma An adjunction, you'll recall, consists of a pair of functors $F\dashv G$ between categories $\mathsf{C}$ and $\mathsf{D}$ together with a bijection of sets, as below, for all objects $X$ in $\mathsf{C}$ and $Y$ in $\mathsf{D}$
Section 4. 24 (0036): Adjoint functors—The Stacks project These maps are called the adjunction maps The adjunction maps are functorial in X and Y, hence we obtain morphisms of functors η: idC → v ∘ u (unit) and ϵ: u ∘ v → idD (counit) Moreover, if α: u(X) → Y and β: X → v(Y) are morphisms, then the following are equivalent
category theory - If adjunction arises everywhere, where is it in the . . . If adjunction, arises everywhere shouldn't we see more examples across the spectrum of maths? For the most part, it seems the example of natural isomorphism that is most widely quoted is that between the category of vector spaces, and its double dual, as discussed here
Adjoint functor - Encyclopedia of Mathematics The functors $ F $ and $ G $ are adjoint, or form an adjoint pair, if $ H ^ {F} $ and $ H _ {G} $ are isomorphic, that is, if there is a natural transformation $ \theta : H ^ {F} \rightarrow H _ {G} $ that establishes a one-to-one correspondence between the sets of morphisms $ H _ {\mathfrak C} ( F (X) , Y ) $ and $ H _ {\mathfrak K} ( X , G (Y)
Adjoint - Wikipedia In mathematics, the term adjoint applies in several situations Several of these share a similar formalism: if A is adjoint to B, then there is typically some formula of the type (Ax, y) = (x, By) Specifically, adjoint or adjunction may mean:
adjunction - Wiktionary, the free dictionary adjunction (countable and uncountable, plural adjunctions) The act of joining; the thing joined or added (law) The joining of personal property owned by one to that owned by another (mathematics, chiefly algebra and number theory) The process of adjoining elements to an algebraic structure (usually a ring or field); the result of such a process
Adjunction: Clear Definition, Examples, And How Its Used As A Figure . . . Adjunction refers to the placement of a word, phrase, or clause at the beginning or end of a sentence The term comes from the Latin words ad (meaning “to” or “towards”) and jungere (meaning “to join”), reflecting the idea of adding or joining elements to a sentence