in category theory, a closed monoidal category (or a monoidal closed category) is a category that is both a monoidal category and a closed category in...

In mathematics, a monoidal category (or tensor category) is a category C {\displaystyle \mathbf {C} } equipped with a bifunctor ⊗ : C × C → C {\displaystyle...

mathematics, a commutativity constraint γ {\displaystyle \gamma } on a monoidal category C {\displaystyle {\mathcal {C}}} is a choice of isomorphism γ A ,...

In category theory, a branch of mathematics, a symmetric monoidal category is a monoidal category (i.e. a category in which a "tensor product" ⊗ {\displaystyle...

is the simply typed lambda calculus. They are generalized by closed monoidal categories, whose internal language, linear type systems, are suitable for...

monoidal structure. A symmetric monoidal category ( C , ⊗ , I ) {\displaystyle (\mathbf {C} ,\otimes ,I)} is compact closed if every object A ∈ C {\displaystyle...

(i.e., making the category symmetric monoidal or even symmetric closed monoidal, respectively).[citation needed] Enriched category theory thus encompasses...

More generally, any monoidal closed category is a closed category. In this case, the object I {\displaystyle I} is the monoidal unit. Eilenberg, S.;...

as category theory, a monoidal category where the monoidal ("tensor") product is the categorical product is called a cartesian monoidal category. Any...

In the mathematical field of category theory, a dagger symmetric monoidal category is a monoidal category ⟨ C , ⊗ , I ⟩ {\displaystyle \langle \mathbf...

there are categories in which currying is not possible; the most general categories which allow currying are the closed monoidal categories. Some programming...

In category theory, monoidal functors are functors between monoidal categories which preserve the monoidal structure. More specifically, a monoidal functor...

In category theory, a traced monoidal category is a category with some extra structure which gives a reasonable notion of feedback. A traced symmetric...

obvious example of a preadditive category is the category Ab itself. More precisely, Ab is a closed monoidal category. Note that commutativity is crucial...

mathematics, a *-autonomous (read "star-autonomous") category C is a symmetric monoidal closed category equipped with a dualizing object ⊥ {\displaystyle...

more detail, this means that a category C is pre-abelian if: C is preadditive, that is enriched over the monoidal category of abelian groups (equivalently...

certain coherence conditions (see symmetric monoidal category for details). A monoidal category is compact closed, if every object A ∈ C {\displaystyle A\in...

product functor defining a monoidal category. The isomorphism is natural in both X and Z. In other words, in a closed monoidal category, the internal Hom functor...

notion of product, Ab is a closed symmetric monoidal category. Ab is not a topos since e.g. it has a zero object. Category of modules Abelian sheaf —...

category Triangulated category Model category 2-category Dagger symmetric monoidal category Dagger compact category Strongly ribbon category Closed monoidal...

is monoidal closed, if one defines both the monoidal product A ⊗ B and the internal hom A ⇒ B by the cartesian product of sets. It is also a monoidal category...

category theory, a branch of mathematics, a dual object is an analogue of a dual vector space from linear algebra for objects in arbitrary monoidal categories...

closed model categories is sometimes thought of as homotopical algebra. The definition given initially by Quillen was that of a closed model category...

monoidal category. The construction of the derived morphisms of one variable will work in a closed monoidal category. The category of sets is closed monoidal...

one-object categories, into FinVect. DisCoCat models are monoidal functors from a pregroup grammar to FinVect. FinSet ZX-calculus category of modules...

mathematics known as category theory, a cosmos is a symmetric closed monoidal category that is complete and cocomplete. Enriched category theory is often considered...

football club based in Mbabane Cosmos (category theory), a complete and cocomplete symmetric closed monoidal category in mathematics Cosmos (plant), a genus...

in category theory, where it is right adjoint to currying in closed monoidal categories. A special case of this are the Cartesian closed categories, whose...

of a commutative monoid; a category with finite coproducts is an example of a symmetric monoidal category. If the category has a zero object Z {\displaystyle...

consider a 2-category with a single object; these are essentially monoidal categories. Bicategories are a weaker notion of 2-dimensional categories in which...