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- Element_(category_theory) abstract "In category theory, the concept of an element, or a point, generalizes the more usual set theoretic concept of an element of a set to an object of any category. This idea often allows to restate definitions or properties of morphisms (such as monomorphism or product) which are given by a universal property in more familiar terms by stating their relation to elements. Some very general theorems, such as Yoneda's lemma and the Mitchell embedding theorem, are of great utility in this way, by allowing one to work in a context where these translations are valid. This approach to category theory, in particular the use of the Yoneda lemma in this way, is due to Grothendieck, and is often called the method of the functor of points.".
- Element_(category_theory) wikiPageExternalLink tr12.pdf.
- Element_(category_theory) wikiPageID "11494409".
- Element_(category_theory) wikiPageLength "6242".
- Element_(category_theory) wikiPageOutDegree "31".
- Element_(category_theory) wikiPageRevisionID "682076836".
- Element_(category_theory) wikiPageWikiLink Abelian_categories.
- Element_(category_theory) wikiPageWikiLink Abelian_category.
- Element_(category_theory) wikiPageWikiLink Alexander_Grothendieck.
- Element_(category_theory) wikiPageWikiLink Algebraic_geometry.
- Element_(category_theory) wikiPageWikiLink Algebraic_variety.
- Element_(category_theory) wikiPageWikiLink Arithmetic_geometry.
- Element_(category_theory) wikiPageWikiLink Category:Category_theory.
- Element_(category_theory) wikiPageWikiLink Category_(mathematics).
- Element_(category_theory) wikiPageWikiLink Category_theory.
- Element_(category_theory) wikiPageWikiLink Complex_number.
- Element_(category_theory) wikiPageWikiLink Complex_numbers.
- Element_(category_theory) wikiPageWikiLink Coproduct.
- Element_(category_theory) wikiPageWikiLink Dual_(category_theory).
- Element_(category_theory) wikiPageWikiLink Element_(mathematics).
- Element_(category_theory) wikiPageWikiLink Epimorphism.
- Element_(category_theory) wikiPageWikiLink Equivalence_relation.
- Element_(category_theory) wikiPageWikiLink Finite_field.
- Element_(category_theory) wikiPageWikiLink Glossary_of_arithmetic_and_Diophantine_geometry.
- Element_(category_theory) wikiPageWikiLink Grothendieck.
- Element_(category_theory) wikiPageWikiLink Injective_function.
- Element_(category_theory) wikiPageWikiLink Integer.
- Element_(category_theory) wikiPageWikiLink Mitchell_embedding_theorem.
- Element_(category_theory) wikiPageWikiLink Mitchells_embedding_theorem.
- Element_(category_theory) wikiPageWikiLink Monomorphism.
- Element_(category_theory) wikiPageWikiLink Product_(category_theory).
- Element_(category_theory) wikiPageWikiLink Rational_number.
- Element_(category_theory) wikiPageWikiLink Real_number.
- Element_(category_theory) wikiPageWikiLink Real_numbers.
- Element_(category_theory) wikiPageWikiLink Scheme_(mathematics).
- Element_(category_theory) wikiPageWikiLink Set_theory.
- Element_(category_theory) wikiPageWikiLink Universal_property.
- Element_(category_theory) wikiPageWikiLink Yoneda_lemma.
- Element_(category_theory) wikiPageWikiLink Yonedas_lemma.
- Element_(category_theory) wikiPageWikiLinkText "Element (category theory)".
- Element_(category_theory) wikiPageWikiLinkText "Element".
- Element_(category_theory) wikiPageWikiLinkText "element".
- Element_(category_theory) hasPhotoCollection Element_(category_theory).
- Element_(category_theory) wikiPageUsesTemplate Template:Cite_book.
- Element_(category_theory) wikiPageUsesTemplate Template:See_also.
- Element_(category_theory) subject Category:Category_theory.
- Element_(category_theory) type Thing.
- Element_(category_theory) comment "In category theory, the concept of an element, or a point, generalizes the more usual set theoretic concept of an element of a set to an object of any category. This idea often allows to restate definitions or properties of morphisms (such as monomorphism or product) which are given by a universal property in more familiar terms by stating their relation to elements.".
- Element_(category_theory) label "Element (category theory)".
- Element_(category_theory) seeAlso Rational_point.
- Element_(category_theory) sameAs m.02rfs_1.
- Element_(category_theory) sameAs Элемент_(теория_категорий).
- Element_(category_theory) sameAs Q5358816.
- Element_(category_theory) sameAs Q5358816.
- Element_(category_theory) wasDerivedFrom Element_(category_theory)?oldid=682076836.
- Element_(category_theory) isPrimaryTopicOf Element_(category_theory).