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Coalgebra

In mathematics, coalgebras or cogebras are structures that are dual (in the category-theoretic sense of reversing arrows) to unital associative algebras. The axioms of unital associative algebras can be formulated in terms of commutative diagrams. Turning all arrows around, one obtains the axioms of coalgebras. Every coalgebra, by (vector space) duality…

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Sweedler notation

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Coalgebra

Nodes68
Edges67
Triples79
Avg. degree1.97
Density0.029412
Components1

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Coalgebra

Top relations

related to Further reading · 48
Coalgebra → Algebra, American Mathematical Society, An, Applied Algebra, Applied Mathematics, Appliquées, Berlin, Block, Bourbaki, Coalgebras, Cofree, Constantin, Generalized, Gómez-Torrecillas, Hopf, Hopf Algebras, III, ISBN, ISSN, José
related to Informal discussion · 10
Coalgebra → Clebsch, For, Given, Gordan, In, It, One, That, The, This
related to Examples · 4
Coalgebra → Define By, K-vector, Take, The
related to Further concepts and facts · 4
Coalgebra → Delta, In Sweedler's, It's, K-linear
related to Sweedler notation · 4
Coalgebra → Delta, Given, Note, When
related to Formal definition · 3
Coalgebra → Delta, Formally, K-linear
is a · 2
Coalgebra → algebra, dual object of an algebra and conversely
related to Finite dimensions · 2
Coalgebra → In, The
related to External links · 1
Coalgebra → William Chin
see also · 1
Coalgebra → Cofree

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Important terminology

algebra coalgebras algebras one coproduct representation unital displaystyle product space associative dual tensor finite-dimensional general zbl finite two form case

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Coalgebrais adual object of an algebra and conversely0.90text
Coalgebrais aalgebra0.90text
Coalgebrarelated to ExamplesTake0.60section
Coalgebrarelated to ExamplesK-vector0.60section
Coalgebrarelated to ExamplesThe0.60section
Coalgebrarelated to ExamplesDefine By0.60section
Coalgebrarelated to External linksWilliam Chin0.60section
Coalgebrarelated to Finite dimensionsIn0.60section
Coalgebrarelated to Finite dimensionsThe0.60section
Coalgebrarelated to Formal definitionFormally0.60section
Coalgebrarelated to Formal definitionK-linear0.60section
Coalgebrarelated to Formal definitionDelta0.60section

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