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- Category_of_preordered_sets abstract "The category Ord has preordered sets as objects and monotonic functions as morphisms. This is a category because the composition of two monotonic functions is monotonic and the identity map is monotonic.The monomorphisms in Ord are the injective monotonic functions.The empty set (considered as a preordered set) is the initial object of Ord; any singleton preordered set is a terminal object. There are thus no zero objects in Ord.The product in Ord is given by the product order on the cartesian product.We have a forgetful functor Ord → Set which assigns to each preordered set the underlying set, and to each monotonic function the underlying function. This functor is faithful, and therefore Ord is a concrete category. This functor has a left adjoint (sending every set to that set equipped with the equality relation) and a right adjoint (sending every set to that set equipped with the total relation).".
- Category_of_preordered_sets wikiPageID "540904".
- Category_of_preordered_sets wikiPageLength "2248".
- Category_of_preordered_sets wikiPageOutDegree "29".
- Category_of_preordered_sets wikiPageRevisionID "661259725".
- Category_of_preordered_sets wikiPageWikiLink 2-category.
- Category_of_preordered_sets wikiPageWikiLink Adjoint_functors.
- Category_of_preordered_sets wikiPageWikiLink Cartesian_product.
- Category_of_preordered_sets wikiPageWikiLink Category:Category-theoretic_categories.
- Category_of_preordered_sets wikiPageWikiLink Category_(mathematics).
- Category_of_preordered_sets wikiPageWikiLink Category_of_sets.
- Category_of_preordered_sets wikiPageWikiLink Category_theory.
- Category_of_preordered_sets wikiPageWikiLink Concrete_category.
- Category_of_preordered_sets wikiPageWikiLink Empty_set.
- Category_of_preordered_sets wikiPageWikiLink Faithful_functor.
- Category_of_preordered_sets wikiPageWikiLink FinOrd.
- Category_of_preordered_sets wikiPageWikiLink FinSet.
- Category_of_preordered_sets wikiPageWikiLink Forgetful_functor.
- Category_of_preordered_sets wikiPageWikiLink Full_and_faithful_functors.
- Category_of_preordered_sets wikiPageWikiLink Function_(mathematics).
- Category_of_preordered_sets wikiPageWikiLink Function_composition.
- Category_of_preordered_sets wikiPageWikiLink Initial_and_terminal_objects.
- Category_of_preordered_sets wikiPageWikiLink Initial_object.
- Category_of_preordered_sets wikiPageWikiLink Injective.
- Category_of_preordered_sets wikiPageWikiLink Injective_function.
- Category_of_preordered_sets wikiPageWikiLink Monomorphism.
- Category_of_preordered_sets wikiPageWikiLink Monotonic_function.
- Category_of_preordered_sets wikiPageWikiLink Morphism.
- Category_of_preordered_sets wikiPageWikiLink Object_(category_theory).
- Category_of_preordered_sets wikiPageWikiLink Posetal_category.
- Category_of_preordered_sets wikiPageWikiLink Preorder.
- Category_of_preordered_sets wikiPageWikiLink Product_(category_theory).
- Category_of_preordered_sets wikiPageWikiLink Product_order.
- Category_of_preordered_sets wikiPageWikiLink Pseudofunctor.
- Category_of_preordered_sets wikiPageWikiLink Set_(mathematics).
- Category_of_preordered_sets wikiPageWikiLink Simplex_category.
- Category_of_preordered_sets wikiPageWikiLink Singleton_(mathematics).
- Category_of_preordered_sets wikiPageWikiLink Terminal_object.
- Category_of_preordered_sets wikiPageWikiLink Zero_object.
- Category_of_preordered_sets wikiPageWikiLinkText "Category of preordered sets".
- Category_of_preordered_sets wikiPageWikiLinkText "Ord".
- Category_of_preordered_sets wikiPageWikiLinkText "category of preordered sets".
- Category_of_preordered_sets hasPhotoCollection Category_of_preordered_sets.
- Category_of_preordered_sets wikiPageUsesTemplate Template:Unreferenced.
- Category_of_preordered_sets subject Category:Category-theoretic_categories.
- Category_of_preordered_sets type Article.
- Category_of_preordered_sets type Article.
- Category_of_preordered_sets comment "The category Ord has preordered sets as objects and monotonic functions as morphisms. This is a category because the composition of two monotonic functions is monotonic and the identity map is monotonic.The monomorphisms in Ord are the injective monotonic functions.The empty set (considered as a preordered set) is the initial object of Ord; any singleton preordered set is a terminal object.".
- Category_of_preordered_sets label "Category of preordered sets".
- Category_of_preordered_sets sameAs Categoría_de_conjuntos_preordenados.
- Category_of_preordered_sets sameAs m.02n51l.
- Category_of_preordered_sets sameAs Q5051853.
- Category_of_preordered_sets sameAs Q5051853.
- Category_of_preordered_sets sameAs 预序范畴.
- Category_of_preordered_sets wasDerivedFrom Category_of_preordered_sets?oldid=661259725.
- Category_of_preordered_sets isPrimaryTopicOf Category_of_preordered_sets.