Anagram & Information om | Engelska ordet COUNIT

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• Specifically, the comultiplication and the counit are both unital algebra homomorphisms, or equivalently, the multiplication and the unit of the algebra both are coalgebra morphisms.
• The representation theory of a Hopf algebra is particularly nice, since the existence of compatible comultiplication, counit, and antipode allows for the construction of tensor products of representations, trivial representations, and dual representations.
• The key property that one has to prove here is that the counit of an adjunction is an isomorphism if and only if the right adjoint is a full and faithful functor.
• This is the motivation for the definition of a bialgebra, where Δ is called the comultiplication and ε is called the counit.
• The existence theorem for the twisted inverse image is the name given to the proof of the existence for what would be the counit for the comonad of the sought-for adjunction, namely a natural transformation.
• Like all adjunctions, the tensor-hom adjunction can be described by its counit and unit natural transformations.
• We give kG the structure of a cocommutative Hopf algebra by defining the coproduct, counit, and antipode to be the linear extensions of the following maps defined on G:.

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