In mathematics, coalgebras or cogebras are structures that are dual (in the category-theoretic sense of reversing arrows) to unital associative algebras...
20 KB (2,899 words) - 20:34, 13 May 2024
mathematics, specifically in category theory, an F {\displaystyle F} -coalgebra is a structure defined according to a functor F {\displaystyle F} , with...
7 KB (929 words) - 15:33, 5 June 2024
measuring coalgebra of two algebras A and B is a coalgebra enrichment of the set of homomorphisms from A to B. In other words, if coalgebras are thought...
3 KB (407 words) - 01:50, 3 December 2023
algebra, the cofree coalgebra of a vector space or module is a coalgebra analog of the free algebra of a vector space. The cofree coalgebra of any vector space...
9 KB (1,708 words) - 02:52, 29 November 2023
Tensor algebra (redirect from Tensor coalgebra)
also has two coalgebra structures; one simple one, which does not make it a bialgebra, but does lead to the concept of a cofree coalgebra, and a more complicated...
23 KB (4,160 words) - 15:09, 12 January 2024
Comodule (redirect from Comodule over a coalgebra)
comodule over a coalgebra is formed by dualizing the definition of a module over an associative algebra. Let K be a field, and C be a coalgebra over K. A (right)...
5 KB (814 words) - 01:25, 13 November 2023
In mathematics a Lie coalgebra is the dual structure to a Lie algebra. In finite dimensions, these are dual objects: the dual vector space to a Lie algebra...
5 KB (1,030 words) - 11:52, 9 June 2021
Coinduction (section Relationship with F-coalgebras)
{\displaystyle F(f)=\langle \mathrm {id} _{A},f\rangle } The final F-coalgebra ν F {\displaystyle \nu F} has the following morphism associated with it:...
13 KB (1,896 words) - 07:11, 22 April 2024
(termination), in computer program termination analysis Measuring coalgebra, a coalgebra constructed from two algebras Measure (Apple), an iOS augmented...
2 KB (279 words) - 19:20, 14 July 2024
Initial algebra (redirect from Final coalgebra)
list object, respectively. Dually, a final coalgebra is a terminal object in the category of F-coalgebras. The finality provides a general framework for...
9 KB (1,144 words) - 21:15, 2 June 2024
Bialgebra (category Coalgebras)
which is both a unital associative algebra and a counital coassociative coalgebra.: 46 The algebraic and coalgebraic structures are made compatible with...
12 KB (1,612 words) - 10:08, 11 April 2024
a coinductive type denotes the assignment of a coalgebra to its unique morphism to the final coalgebra of an endofunctor. These objects are used in functional...
9 KB (1,260 words) - 17:45, 16 August 2022
Transition system (section Coalgebra formulation)
{\alpha } q\,\}} . In other words, a labelled state transition system is a coalgebra for the functor P ( Λ × − ) {\displaystyle P(\Lambda \times {-})} . There...
6 KB (859 words) - 05:34, 2 June 2024
Associative algebra (section Coalgebras)
structure of a coalgebra. There is also an abstract notion of F-coalgebra, where F is a functor. This is vaguely related to the notion of coalgebra discussed...
31 KB (4,449 words) - 08:23, 9 August 2024
simultaneously an (unital associative) algebra and a (counital coassociative) coalgebra, with these structures' compatibility making it a bialgebra, and that...
35 KB (4,397 words) - 02:43, 12 April 2024
F-algebra (section Terminal F-coalgebra)
serve to encapsulate the induction principle, and the dual construction F-coalgebras. If C {\displaystyle C} is a category, and F : C → C {\displaystyle F:C\rightarrow...
14 KB (1,800 words) - 00:32, 6 March 2024
unary involution operation Von Neumann algebra (or W*-algebra) See also coalgebra, the dual notion. A different class of "algebras" consists of objects...
3 KB (415 words) - 17:08, 30 November 2021
C*-algebra Composition algebra Computer algebra Exterior algebra F-algebra F-coalgebra Heyting algebra Hopf algebra Non-associative algebra Outline of algebra...
135 KB (13,094 words) - 18:43, 14 August 2024
integer multiple of another element in the lattice Primitive element (coalgebra), an element X on which the comultiplication Δ has the value Δ(X) = X⊗1...
832 bytes (140 words) - 08:53, 23 April 2020
From an initial algebra to an algebra: Catamorphism From a coalgebra to a final coalgebra: Anamorphism An anamorphism followed by an catamorphism: Hylomorphism...
3 KB (305 words) - 19:14, 8 June 2022
product), is a unital associative K-algebra, and a comonoid object is a K-coalgebra. For any category C, the category [C, C] of its endofunctors has a monoidal...
5 KB (511 words) - 14:20, 31 January 2024
From an initial algebra to an algebra: Catamorphism From a coalgebra to a final coalgebra: Anamorphism Extension of the idea of catamorphisms: Paramorphism...
5 KB (716 words) - 00:17, 24 January 2024
cohomology Lie algebra extension Lie algebra representation Lie bialgebra Lie coalgebra Lie operad Particle physics and representation theory Lie superalgebra...
61 KB (10,457 words) - 02:56, 14 July 2024
publications indexed by Google Scholar Silva, Alexandra (2010). Kleene coalgebra (PDF). ru.nl (PhD thesis). 694079062. hdl:2066/83205. OCLC 694079062....
3 KB (171 words) - 12:09, 18 October 2022
mathematics, the coidentity of a dual group object or the counit of a coalgebra In sociology, double consciousness This disambiguation page lists articles...
234 bytes (65 words) - 14:19, 12 April 2024
sets. Free algebras over division rings are free ideal rings. Cofree coalgebra Tensor algebra Free object Noncommutative ring Rational series Term algebra...
6 KB (915 words) - 09:19, 17 May 2024
usual tensor product are important and widely studied under the name of coalgebras. The notion of monad was invented by Roger Godement in 1958 under the...
30 KB (4,467 words) - 15:23, 8 August 2024
algebra, and C {\displaystyle C} a right H {\displaystyle H} -module coalgebra. A left-right Doi-Hopf ( H , A , C ) {\displaystyle (H,A,C)} -module M...
2 KB (319 words) - 06:44, 23 December 2023
\phi _{2}(X)} . This product can be recognized as the coproduct on a coalgebra. In general, the tensor product of irreducible representations is not...
55 KB (7,184 words) - 17:41, 8 July 2024
From an initial algebra to an algebra: Catamorphism From a coalgebra to a final coalgebra: Anamorphism An anamorphism followed by an catamorphism: Hylomorphism...
1 KB (122 words) - 22:23, 17 December 2018