• 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...
    7 KB (1,167 words) - 18:33, 17 September 2023
  • In mathematics, a monoidal category (or tensor category) is a category C {\displaystyle \mathbf {C} } equipped with a bifunctor ⊗ : C × C → C {\displaystyle...
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  • mathematics, a commutativity constraint γ {\displaystyle \gamma } on a monoidal category C {\displaystyle {\mathcal {C}}} is a choice of isomorphism γ A ,...
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  • 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...
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  • is the simply typed lambda calculus. They are generalized by closed monoidal categories, whose internal language, linear type systems, are suitable for...
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  • monoidal structure. A symmetric monoidal category ( C , ⊗ , I ) {\displaystyle (\mathbf {C} ,\otimes ,I)} is compact closed if every object A ∈ C {\displaystyle...
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  • (i.e., making the category symmetric monoidal or even symmetric closed monoidal, respectively).[citation needed] Enriched category theory thus encompasses...
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  • More generally, any monoidal closed category is a closed category. In this case, the object I {\displaystyle I} is the monoidal unit. Eilenberg, S.;...
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  • as category theory, a monoidal category where the monoidal ("tensor") product is the categorical product is called a cartesian monoidal category. Any...
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  • In the mathematical field of category theory, a dagger symmetric monoidal category is a monoidal category ⟨ C , ⊗ , I ⟩ {\displaystyle \langle \mathbf...
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  • Thumbnail for 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...
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  • In category theory, monoidal functors are functors between monoidal categories which preserve the monoidal structure. More specifically, a monoidal functor...
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  • there are categories in which currying is not possible; the most general categories which allow currying are the closed monoidal categories. Some programming...
    36 KB (5,025 words) - 06:35, 27 September 2024
  • mathematics, a *-autonomous (read "star-autonomous") category C is a symmetric monoidal closed category equipped with a dualizing object ⊥ {\displaystyle...
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  • obvious example of a preadditive category is the category Ab itself. More precisely, Ab is a closed monoidal category. Note that commutativity is crucial...
    12 KB (1,667 words) - 22:11, 28 October 2024
  • 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...
    10 KB (1,382 words) - 03:45, 26 March 2024
  • certain coherence conditions (see symmetric monoidal category for details). A monoidal category is compact closed, if every object A ∈ C {\displaystyle A\in...
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  • 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...
    10 KB (1,056 words) - 03:31, 25 October 2024
  • 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 —...
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  • category Triangulated category Model category 2-category Dagger symmetric monoidal category Dagger compact category Strongly ribbon category Closed monoidal...
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  • Thumbnail for Category of relations
    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...
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  • Dual object (redirect from Pivotal 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...
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  • closed model categories is sometimes thought of as homotopical algebra. The definition given initially by Quillen was that of a closed model category...
    18 KB (2,402 words) - 15:12, 12 October 2024
  • 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...
    7 KB (1,054 words) - 00:10, 11 January 2024
  • one-object categories, into FinVect. DisCoCat models are monoidal functors from a pregroup grammar to FinVect. FinSet ZX-calculus category of modules...
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  • mathematics known as category theory, a cosmos is a symmetric closed monoidal category that is complete and cocomplete. Enriched category theory is often considered...
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  • football club based in Mbabane Cosmos (category theory), a complete and cocomplete symmetric closed monoidal category in mathematics Cosmos (plant), a genus...
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  • 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...
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  • Thumbnail for Category theory
    consider a 2-category with a single object; these are essentially monoidal categories. Bicategories are a weaker notion of 2-dimensional categories in which...
    34 KB (3,836 words) - 00:38, 21 December 2024
  • In mathematics, a fusion category is a category that is abelian, k {\displaystyle k} -linear, semisimple, monoidal, and rigid, and has only finitely many...
    2 KB (187 words) - 21:50, 28 July 2024