Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Monoidal_category> ?p ?o. }
Showing items 1 to 37 of
37
with 100 items per page.
- Monoidal_category abstract "In mathematics, a monoidal category (or tensor category) is a category C equipped with a bifunctor⊗ : C × C → Cwhich is associative, up to a natural isomorphism, and an object I which is both a left and right identity for ⊗, again up to a natural isomorphism. The associated natural isomorphisms are subject to certain coherence conditions which ensure that all the relevant diagrams commute.In a monoidal category, analogs of usual monoids from abstract algebra can be defined using the same commutative diagrams. In fact, usual monoids are exactly the monoid objects in the monoidal category of sets with Cartesian product.The ordinary tensor product makes vector spaces, abelian groups, R-modules, or R-algebras into monoidal categories. Monoidal categories can be seen as a generalization of these and other examples.In category theory, monoidal categories can be used to define the concept of a monoid object and an associated action on the objects of the category. They are also used in the definition of an enriched category.Monoidal categories have numerous applications outside of category theory proper. They are used to define models for the multiplicative fragment of intuitionistic linear logic. They also form the mathematical foundation for the topological order in condensed matter. Braided monoidal categories have applications in quantum field theory and string theory.".
- Monoidal_category thumbnail Monoidal-category-pentagon.png?width=300.
- Monoidal_category wikiPageExternalLink tr10.pdf.
- Monoidal_category wikiPageID "330604".
- Monoidal_category wikiPageRevisionID "599900548".
- Monoidal_category hasPhotoCollection Monoidal_category.
- Monoidal_category id "monoidal+category".
- Monoidal_category title "Monoidal category".
- Monoidal_category subject Category:Monoidal_categories.
- Monoidal_category type Abstraction100002137.
- Monoidal_category type Class107997703.
- Monoidal_category type Collection107951464.
- Monoidal_category type Group100031264.
- Monoidal_category type MonoidalCategories.
- Monoidal_category comment "In mathematics, a monoidal category (or tensor category) is a category C equipped with a bifunctor⊗ : C × C → Cwhich is associative, up to a natural isomorphism, and an object I which is both a left and right identity for ⊗, again up to a natural isomorphism.".
- Monoidal_category label "Categoria monoidale".
- Monoidal_category label "Categoría monoidal".
- Monoidal_category label "Catégorie monoïdale".
- Monoidal_category label "Monoidal category".
- Monoidal_category label "Monoidale Kategorie".
- Monoidal_category label "Monoïdale categorie".
- Monoidal_category label "Моноидальная категория".
- Monoidal_category label "モノイド圏".
- Monoidal_category label "么半範疇".
- Monoidal_category sameAs Monoidale_Kategorie.
- Monoidal_category sameAs Categoría_monoidal.
- Monoidal_category sameAs Catégorie_monoïdale.
- Monoidal_category sameAs Categoria_monoidale.
- Monoidal_category sameAs モノイド圏.
- Monoidal_category sameAs Monoïdale_categorie.
- Monoidal_category sameAs m.01wvxr.
- Monoidal_category sameAs Q1945014.
- Monoidal_category sameAs Q1945014.
- Monoidal_category sameAs Monoidal_category.
- Monoidal_category wasDerivedFrom Monoidal_category?oldid=599900548.
- Monoidal_category depiction Monoidal-category-pentagon.png.
- Monoidal_category isPrimaryTopicOf Monoidal_category.