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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 wikiPageRevisionID "549824706".
- Category_of_preordered_sets hasPhotoCollection Category_of_preordered_sets.
- Category_of_preordered_sets subject Category:Category-theoretic_categories.
- Category_of_preordered_sets type Abstraction100002137.
- Category_of_preordered_sets type Category-theoreticCategories.
- Category_of_preordered_sets type Class107997703.
- Category_of_preordered_sets type Collection107951464.
- Category_of_preordered_sets type Group100031264.
- 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 label "Categoría de conjuntos preordenados".
- Category_of_preordered_sets label "预序范畴".
- 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 Category_of_preordered_sets.
- Category_of_preordered_sets wasDerivedFrom Category_of_preordered_sets?oldid=549824706.
- Category_of_preordered_sets isPrimaryTopicOf Category_of_preordered_sets.