associative coproduct
1Exterior algebra — In mathematics, the exterior product or wedge product of vectors is an algebraic construction generalizing certain features of the cross product to higher dimensions. Like the cross product, and the scalar triple product, the exterior product of… …
2Category of rings — In mathematics, the category of rings, denoted by Ring, is the category whose objects are rings (with identity) and whose morphisms are ring homomorphisms (preserving the identity). Like many categories in mathematics, the category of rings is… …
3Braided Hopf algebra — In mathematics a braided Hopf algebra is a Hopf algebra in a braided monoidal category. The most common braided Hopf algebras are objects in a Yetter Drinfel d category of a Hopf algebra H . Definition Let H be a Hopf algebra over a field k , and …
4Coalgebra — In mathematics, coalgebras or cogebras are structures that are dual (in the sense of reversing arrows) to unital associative algebras. The axioms of unital associative algebras can be formulated in terms of commutative diagrams. Turning all… …
5Ordinal arithmetic — In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially two different ways: either by constructing an… …
6Addition — is the mathematical process of putting things together. The plus sign + means that two numbers are added together. For example, in the picture on the right, there are 3 + 2 apples meaning three apples and two other apples which is the same as… …
7Direct sum of modules — For the broader use of the term in mathematics, see Direct sum. In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The result of the direct summation of modules is the smallest general… …
8Tensor algebra — In mathematics, the tensor algebra of a vector space V , denoted T ( V ) or T bull;( V ), is the algebra of tensors on V (of any rank) with multiplication being the tensor product. It is the free algebra on V , in the sense of being left adjoint… …
9Tensor product of algebras — In mathematics, the tensor product of two R algebras is also an R algebra in a natural way. This gives us a tensor product of algebras. The special case R = Z gives us a tensor product of rings, since rings may be regarded as Z algebras.Let R be… …
10Quantum group — In mathematics and theoretical physics, quantum groups are certain noncommutative algebras that first appeared in the theory of quantum integrable systems, and which were then formalized by Vladimir Drinfel d and Michio Jimbo. There is no single …
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