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- Concrete_category abstract "In mathematics, a concrete category is a category that is equipped with a faithful functor to the category of sets. This functor makes it possible to think of the objects of the category as sets with additional structure, and of its morphisms as structure-preserving functions. Many important categories have obvious interpretations as concrete categories, for example the category of topological spaces and the category of groups, and trivially also the category of sets itself. On the other hand, the homotopy category of topological spaces is not concretizable, i.e. it does not admit a faithful functor to the category of sets.A concrete category, when defined without reference to the notion of a category, consists of a class of objects, each equipped with an underlying set; and for any two objects A and B a set of functions, called morphisms, from the underlying set of A to the underlying set of B. Furthermore, for every object A, the identity function on the underlying set of A must be a morphism from A to A, and the composition of a morphism from A to B followed by a morphism from B to C must be a morphism from A to C.".
- Concrete_category wikiPageExternalLink acc.pdf.
- Concrete_category wikiPageExternalLink 00224049.
- Concrete_category wikiPageExternalLink tr6abs.html.
- Concrete_category wikiPageID "167001".
- Concrete_category wikiPageRevisionID "591790833".
- Concrete_category hasPhotoCollection Concrete_category.
- Concrete_category subject Category:Category_theory.
- Concrete_category comment "In mathematics, a concrete category is a category that is equipped with a faithful functor to the category of sets. This functor makes it possible to think of the objects of the category as sets with additional structure, and of its morphisms as structure-preserving functions. Many important categories have obvious interpretations as concrete categories, for example the category of topological spaces and the category of groups, and trivially also the category of sets itself.".
- Concrete_category label "Concrete categorie".
- Concrete_category label "Concrete category".
- Concrete_category label "Konkrete Kategorie".
- Concrete_category label "Конкретная категория".
- Concrete_category label "具體範疇".
- Concrete_category sameAs Konkrete_Kategorie.
- Concrete_category sameAs Concrete_categorie.
- Concrete_category sameAs m.0169lb.
- Concrete_category sameAs Q1575634.
- Concrete_category sameAs Q1575634.
- Concrete_category wasDerivedFrom Concrete_category?oldid=591790833.
- Concrete_category isPrimaryTopicOf Concrete_category.