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- Monoid_(category_theory) abstract "In category theory, a monoid (or monoid object) (M, μ, η) in a monoidal category (C, ⊗, I) is an object M together with two morphisms μ: M ⊗ M → M called multiplication, η: I → M called unit,such that the pentagon diagramFile:Monoid multiplication.svgand the unitor diagramFile:Monoid unit svg.svgcommute. In the above notations, I is the unit element and α, λ and ρ are respectively the associativity, the left identity and the right identity of the monoidal category C.Dually, a comonoid in a monoidal category C is a monoid in the dual category Cop.Suppose that the monoidal category C has a symmetry γ. A monoid M in C is commutative when μ o γ = μ.".
- Monoid_(category_theory) thumbnail Monoid_multiplication.svg?width=300.
- Monoid_(category_theory) wikiPageID "3955446".
- Monoid_(category_theory) wikiPageLength "4109".
- Monoid_(category_theory) wikiPageOutDegree "44".
- Monoid_(category_theory) wikiPageRevisionID "702197081".
- Monoid_(category_theory) wikiPageWikiLink Algebra_over_a_field.
- Monoid_(category_theory) wikiPageWikiLink Associative_algebra.
- Monoid_(category_theory) wikiPageWikiLink Category:Category-theoretic_categories.
- Monoid_(category_theory) wikiPageWikiLink Category:Monoidal_categories.
- Monoid_(category_theory) wikiPageWikiLink Category:Objects_(category_theory).
- Monoid_(category_theory) wikiPageWikiLink Category_of_abelian_groups.
- Monoid_(category_theory) wikiPageWikiLink Category_of_magmas.
- Monoid_(category_theory) wikiPageWikiLink Category_of_modules.
- Monoid_(category_theory) wikiPageWikiLink Category_of_sets.
- Monoid_(category_theory) wikiPageWikiLink Category_of_topological_spaces.
- Monoid_(category_theory) wikiPageWikiLink Category_theory.
- Monoid_(category_theory) wikiPageWikiLink Coalgebra.
- Monoid_(category_theory) wikiPageWikiLink Commutative_ring.
- Monoid_(category_theory) wikiPageWikiLink Complete_lattice.
- Monoid_(category_theory) wikiPageWikiLink Coproduct.
- Monoid_(category_theory) wikiPageWikiLink Differential_graded_algebra.
- Monoid_(category_theory) wikiPageWikiLink Dual_(category_theory).
- Monoid_(category_theory) wikiPageWikiLink Eckmann–Hilton_argument.
- Monoid_(category_theory) wikiPageWikiLink Functor.
- Monoid_(category_theory) wikiPageWikiLink Graded_ring.
- Monoid_(category_theory) wikiPageWikiLink Integer.
- Monoid_(category_theory) wikiPageWikiLink Monad_(category_theory).
- Monoid_(category_theory) wikiPageWikiLink Monoid.
- Monoid_(category_theory) wikiPageWikiLink Monoidal_category.
- Monoid_(category_theory) wikiPageWikiLink Morphism.
- Monoid_(category_theory) wikiPageWikiLink Product_(category_theory).
- Monoid_(category_theory) wikiPageWikiLink Product_topology.
- Monoid_(category_theory) wikiPageWikiLink Quantale.
- Monoid_(category_theory) wikiPageWikiLink Ring_(mathematics).
- Monoid_(category_theory) wikiPageWikiLink Semigroup_action.
- Monoid_(category_theory) wikiPageWikiLink Symmetric_monoidal_category.
- Monoid_(category_theory) wikiPageWikiLink Topological_monoid.
- Monoid_(category_theory) wikiPageWikiLink File:Category_monoids_eta.svg.
- Monoid_(category_theory) wikiPageWikiLink File:Category_monoids_mu.svg.
- Monoid_(category_theory) wikiPageWikiLink File:Monoid_multiplication.svg.
- Monoid_(category_theory) wikiPageWikiLink File:Monoid_unit_svg.svg.
- Monoid_(category_theory) wikiPageWikiLinkText "Monoid (category theory)".
- Monoid_(category_theory) wikiPageWikiLinkText "category of monoids".
- Monoid_(category_theory) wikiPageWikiLinkText "monoid (category theory)".
- Monoid_(category_theory) wikiPageWikiLinkText "monoid category".
- Monoid_(category_theory) wikiPageWikiLinkText "monoid object".
- Monoid_(category_theory) wikiPageWikiLinkText "monoid".
- Monoid_(category_theory) wikiPageWikiLinkText "monoids".
- Monoid_(category_theory) wikiPageUsesTemplate Template:Reflist.
- Monoid_(category_theory) subject Category:Category-theoretic_categories.
- Monoid_(category_theory) subject Category:Monoidal_categories.
- Monoid_(category_theory) subject Category:Objects_(category_theory).
- Monoid_(category_theory) comment "In category theory, a monoid (or monoid object) (M, μ, η) in a monoidal category (C, ⊗, I) is an object M together with two morphisms μ: M ⊗ M → M called multiplication, η: I → M called unit,such that the pentagon diagramFile:Monoid multiplication.svgand the unitor diagramFile:Monoid unit svg.svgcommute.".
- Monoid_(category_theory) label "Monoid (category theory)".
- Monoid_(category_theory) sameAs Q2785361.
- Monoid_(category_theory) sameAs Monoid-Objekt.
- Monoid_(category_theory) sameAs Monoïde_(théorie_des_catégories).
- Monoid_(category_theory) sameAs 모노이드_대상.
- Monoid_(category_theory) sameAs Monoïde_(categorietheorie).
- Monoid_(category_theory) sameAs m.0b8hch.
- Monoid_(category_theory) sameAs Моноид_(теория_категорий).
- Monoid_(category_theory) sameAs Q2785361.
- Monoid_(category_theory) wasDerivedFrom Monoid_(category_theory)?oldid=702197081.
- Monoid_(category_theory) depiction Monoid_multiplication.svg.
- Monoid_(category_theory) isPrimaryTopicOf Monoid_(category_theory).