monoidal category
1Monoidal category — In mathematics, a monoidal category (or tensor category) is a category C equipped with a bifunctor ⊗ : C × C → C which is associative, up to a natural isomorphism, and an object I which is both a left and right identity for ⊗, again up to a… …
2Closed monoidal category — In mathematics, especially in category theory, a closed monoidal category is a context where we can take tensor products of objects and also form mapping objects . A classic example is the category of sets, Set, where the tensor product of sets A …
3Dagger symmetric monoidal category — A dagger symmetric monoidal category is a monoidal category which also possesses a dagger structure; in other words, it means that this category comes equipped not only with a tensor in the category theoretic sense but also with dagger structure… …
4Braided monoidal category — In mathematics, a braided monoidal category is a monoidal category C equipped with a braiding; that is, there is a natural isomorphism:gamma {A,B}:Aotimes B ightarrow Botimes Afor which the following hexagonal diagrams commute (here alpha is the… …
5Traced monoidal category — In category theory, a traced monoidal category is a category with some extra structure which gives a reasonable notion of feedback.A traced symmetric monoidal category is a symmetric monoidal category C together with a family of… …
6Monoidal monad — In category theory, a monoidal monad (T,η,μ,m) is a monad (T,η,μ) on a monoidal category such that the functor is a lax monoidal functor with and as coherence maps, and the natu …
7Category 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… …
8Category of vector spaces — In mathematics, especially category theory, the category K Vect has all vector spaces over a fixed field K as objects and K linear transformations as morphisms. If K is the field of real numbers, then the category is also known as Vec.Since… …
9Category of abelian groups — In mathematics, the category Ab has the abelian groups as objects and group homomorphisms as morphisms. This is the prototype of an abelian category.The monomorphisms in Ab are the injective group homomorphisms, the epimorphisms are the… …
10Monoidal functor — In category theory, monoidal functors are functors between monoidal categories which preserve the monoidal structure. More specifically, a monoidal functor between two monoidal categories consists of a functor between the categories, along with… …
