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If the functor F : D → C has two right adjoints G and G′, then G and G′ are naturally isomorphic. The same is true for left adjoints. Conversely, if F is left adjoint to G, and G is naturally isomorphic to G′ then F is also left adjoint to G′. More generally, if 〈F, G, ε, η〉 is an adjunction (with counit–unit (ε,η)) and σ ...
The upper and lower adjoints of a Galois connection in order theory; The adjoint of a differential operator with general polynomial coefficients; ... Mobile view ...
In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space.
In category theory, a branch of mathematics, the formal criteria for adjoint functors are criteria for the existence of a left or right adjoint of a given functor.. One criterion is the following, which first appeared in Peter J. Freyd's 1964 book Abelian Categories, [1] an Introduction to the Theory of Functors:
In linear algebra, the adjugate or classical adjoint of a square matrix A, adj(A), is the transpose of its cofactor matrix. [1] [2] It is occasionally known as adjunct matrix, [3] [4] or "adjoint", [5] though that normally refers to a different concept, the adjoint operator which for a matrix is the conjugate transpose.
According to the New York Times, here's exactly how to play Strands: Find theme words to fill the board. Theme words stay highlighted in blue when found.
In mathematics, the tensor-hom adjunction is that the tensor product and hom-functor (,) form an adjoint pair: (,) (, (,)). This is made more precise below. The order of terms in the phrase "tensor-hom adjunction" reflects their relationship: tensor is the left adjoint, while hom is the right adjoint.
What is the "we listen and we don't judge" trend? Couples tell us if it led to any breakthroughs and a psychologist says if it's healthy.