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- 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 $\mathsf{D}$
- ADJUNCTION Definition Meaning - Merriam-Webster
The meaning of ADJUNCTION is the act or process of adjoining
- 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:
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