# monoidal

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monoidal
Of, pertaining to, or being a monoid.

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• Monoidal t-norm logic — Monoidal t norm based logic (or shortly MTL), the logic of left continuous t norms, is one of t norm fuzzy logics. It belongs to the broader class of substructural logics, or logics of residuated lattices; it extends the logic of commutative… …   Wikipedia

• Monoidal 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… …   Wikipedia

• Monoidal 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… …   Wikipedia

• Monoidal 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 …   Wikipedia

• Monoidal adjunction — Suppose that and are two monoidal categories. A monoidal adjunction between two lax monoidal functors and is an adjunction (F,G,η,ε) between the underlying functors, such that the natural transformations …   Wikipedia

• Monoidal natural transformation — Suppose that and are two monoidal categories and and are two lax monoidal functors between those categories. A monoidal natural transformation between those funct …   Wikipedia

• Closed 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 …   Wikipedia

• Dagger 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… …   Wikipedia

• Braided 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… …   Wikipedia

• Traced 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… …   Wikipedia