Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Category_(mathematics)> ?p ?o }
- Category_(mathematics) abstract "In mathematics, a category is an algebraic structure that comprises \"objects\" that are linked by \"arrows\". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. On the other hand, any monoid can be understood as a special sort of category, and so can any preorder. In general, the objects and arrows may be abstract entities of any kind, and the notion of category provides a fundamental and abstract way to describe mathematical entities and their relationships. This is the central idea of category theory, a branch of mathematics which seeks to generalize all of mathematics in terms of objects and arrows, independent of what the objects and arrows represent. Virtually every branch of modern mathematics can be described in terms of categories, and doing so often reveals deep insights and similarities between seemingly different areas of mathematics. For more extensive motivational background and historical notes, see category theory and the list of category theory topics.Two categories are the same if they have the same collection of objects, the same collection of arrows, and the same associative method of composing any pair of arrows. Two categories may also be considered \"equivalent\" for purposes of category theory, even if they are not precisely the same.Well-known categories are denoted by a short capitalized word or abbreviation in bold or italics: examples include Set, the category of sets and set functions; Ring, the category of rings and ring homomorphisms; and Top, the category of topological spaces and continuous maps. All of the preceding categories have the identity map as identity arrow and composition as the associative operation on arrows.The classic and still much used text on category theory is Categories for the Working Mathematician by Saunders Mac Lane. Other references are given in the References below. The basic definitions in this article are contained within the first few chapters of any of these books.".
- Category_(mathematics) thumbnail Category_SVG.svg?width=300.
- Category_(mathematics) wikiPageExternalLink acc.pdf.
- Category_(mathematics) wikiPageExternalLink tr12abs.html.
- Category_(mathematics) wikiPageExternalLink category-theory.
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- Category_(mathematics) wikiPageRevisionID "688616378".
- Category_(mathematics) wikiPageWikiLink Abelian_category.
- Category_(mathematics) wikiPageWikiLink Abelian_group.
- Category_(mathematics) wikiPageWikiLink Additive_category.
- Category_(mathematics) wikiPageWikiLink Algebraic_structure.
- Category_(mathematics) wikiPageWikiLink Allegory_(category_theory).
- Category_(mathematics) wikiPageWikiLink Associative_property.
- Category_(mathematics) wikiPageWikiLink Automorphism.
- Category_(mathematics) wikiPageWikiLink Bilinear_form.
- Category_(mathematics) wikiPageWikiLink Binary_operation.
- Category_(mathematics) wikiPageWikiLink Binary_relation.
- Category_(mathematics) wikiPageWikiLink Bundle_map.
- Category_(mathematics) wikiPageWikiLink Cartesian_closed_category.
- Category_(mathematics) wikiPageWikiLink Categories_for_the_Working_Mathematician.
- Category_(mathematics) wikiPageWikiLink Category:Category_theory.
- Category_(mathematics) wikiPageWikiLink Category_of_abelian_groups.
- Category_(mathematics) wikiPageWikiLink Category_of_groups.
- Category_(mathematics) wikiPageWikiLink Category_of_magmas.
- Category_(mathematics) wikiPageWikiLink Category_of_manifolds.
- Category_(mathematics) wikiPageWikiLink Category_of_metric_spaces.
- Category_(mathematics) wikiPageWikiLink Category_of_modules.
- Category_(mathematics) wikiPageWikiLink Category_of_preordered_sets.
- Category_(mathematics) wikiPageWikiLink Category_of_relations.
- Category_(mathematics) wikiPageWikiLink Category_of_rings.
- Category_(mathematics) wikiPageWikiLink Category_of_sets.
- Category_(mathematics) wikiPageWikiLink Category_of_small_categories.
- Category_(mathematics) wikiPageWikiLink Category_of_topological_spaces.
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- Category_(mathematics) wikiPageWikiLink Class_(set_theory).
- Category_(mathematics) wikiPageWikiLink Cokernel.
- Category_(mathematics) wikiPageWikiLink Commutative_diagram.
- Category_(mathematics) wikiPageWikiLink Complete_category.
- Category_(mathematics) wikiPageWikiLink Complete_partial_order.
- Category_(mathematics) wikiPageWikiLink Concrete_category.
- Category_(mathematics) wikiPageWikiLink Continuous_function.
- Category_(mathematics) wikiPageWikiLink Coproduct.
- Category_(mathematics) wikiPageWikiLink Differentiable_manifold.
- Category_(mathematics) wikiPageWikiLink Directed_graph.
- Category_(mathematics) wikiPageWikiLink Discrete_category.
- Category_(mathematics) wikiPageWikiLink Dual_(category_theory).
- Category_(mathematics) wikiPageWikiLink Endomorphism.
- Category_(mathematics) wikiPageWikiLink Enriched_category.
- Category_(mathematics) wikiPageWikiLink Epimorphism.
- Category_(mathematics) wikiPageWikiLink Equivalence_of_categories.
- Category_(mathematics) wikiPageWikiLink Equivalence_relation.
- Category_(mathematics) wikiPageWikiLink Fiber_bundle.
- Category_(mathematics) wikiPageWikiLink Field_(mathematics).
- Category_(mathematics) wikiPageWikiLink Free_category.
- Category_(mathematics) wikiPageWikiLink Function_(mathematics).
- Category_(mathematics) wikiPageWikiLink Function_composition.
- Category_(mathematics) wikiPageWikiLink Functor.
- Category_(mathematics) wikiPageWikiLink GNU_Free_Documentation_License.
- Category_(mathematics) wikiPageWikiLink Generator_(mathematics).
- Category_(mathematics) wikiPageWikiLink Group_(mathematics).
- Category_(mathematics) wikiPageWikiLink Group_action.
- Category_(mathematics) wikiPageWikiLink Group_homomorphism.
- Category_(mathematics) wikiPageWikiLink Groupoid.
- Category_(mathematics) wikiPageWikiLink Higher_category_theory.
- Category_(mathematics) wikiPageWikiLink Identity_(mathematics).
- Category_(mathematics) wikiPageWikiLink Identity_element.
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- Category_(mathematics) wikiPageWikiLink Isomorphism.
- Category_(mathematics) wikiPageWikiLink Kernel_(category_theory).
- Category_(mathematics) wikiPageWikiLink Limit_(category_theory).
- Category_(mathematics) wikiPageWikiLink Linear_map.
- Category_(mathematics) wikiPageWikiLink List_of_mathematical_symbols.
- Category_(mathematics) wikiPageWikiLink Loop_(graph_theory).
- Category_(mathematics) wikiPageWikiLink Magma_(algebra).
- Category_(mathematics) wikiPageWikiLink Mathematics.
- Category_(mathematics) wikiPageWikiLink Metric_map.
- Category_(mathematics) wikiPageWikiLink Metric_space.
- Category_(mathematics) wikiPageWikiLink Module_(mathematics).
- Category_(mathematics) wikiPageWikiLink Module_homomorphism.
- Category_(mathematics) wikiPageWikiLink Monoid.
- Category_(mathematics) wikiPageWikiLink Monomorphism.
- Category_(mathematics) wikiPageWikiLink Monotonic_function.
- Category_(mathematics) wikiPageWikiLink Morphism.
- Category_(mathematics) wikiPageWikiLink Ordinal_number.
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- Category_(mathematics) wikiPageWikiLink Partially_ordered_set.
- Category_(mathematics) wikiPageWikiLink Preadditive_category.
- Category_(mathematics) wikiPageWikiLink Preorder.
- Category_(mathematics) wikiPageWikiLink Product_(category_theory).
- Category_(mathematics) wikiPageWikiLink Quantaloid.
- Category_(mathematics) wikiPageWikiLink Reflexive_relation.
- Category_(mathematics) wikiPageWikiLink Ring_(mathematics).
- Category_(mathematics) wikiPageWikiLink Ring_homomorphism.
- Category_(mathematics) wikiPageWikiLink Samuel_Eilenberg.
- Category_(mathematics) wikiPageWikiLink Saunders_Mac_Lane.
- Category_(mathematics) wikiPageWikiLink Scott_continuity.
- Category_(mathematics) wikiPageWikiLink Section_(category_theory).
- Category_(mathematics) wikiPageWikiLink Set_(mathematics).