In mathematics, coalgebras or cogebras are structures that are dual (in the category-theoretic sense of reversing arrows) to unital associative algebras...

mathematics, specifically in category theory, an F {\displaystyle F} -coalgebra is a structure defined according to a functor F {\displaystyle F} , with...

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...

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...

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...

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)...

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...

list object, respectively. Dually, a final coalgebra is a terminal object in the category of F-coalgebras. The finality provides a general framework for...

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...

which is both a unital associative algebra and a counital coassociative coalgebra.: 46  The algebraic and coalgebraic structures are made compatible with...