Note: The translation for this entry is currently under quality review. Some content is temporarily displayed in English only.
groupoid
groupoid
Danh từ
Số nhiều: groupoids
This term is used exclusively within the specialized domain of category theory and abstract algebra. It describes a structure that generalizes the concept of a group by relaxing the requirement that the binary operation be defined for all pairs of elements, making it a partial operation instead.
In a mathematical context, a groupoid can be viewed as a category where every morphism is an isomorphism. This distinction is crucial for researchers in differential geometry and topology, where groupoids are employed to model symmetries and equivalence relations that cannot be captured by standard group theory.
Ý nghĩa
Từ liên quan
algebragroupmagmasemigroupmonoidcategorycategory theorymorphismisomorphismautomorphisminverseidentitybinary operationcompositionassociativityelementsetstructureaxiomtheoremproofmappingfunctiondomaincodomainkernelimagequotientsubgrouphomomorphismendomorphismequivalence relationpartitionbundlemanifoldtopologyhomeomorphismdiffeomorphismoperatortransformationpermutationsymmetryinvarianttensormoduleringfieldlatticeboolean algebrafunctornatural transformationadjunctiondualunitgraphdirected graphpathcycleorbitstabilizercosetnormal subgroupcentercommutatorabelian group