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...'' is [[Adjoint functors|right adjoint]] to the [[forgetful functor]] from coalgebras to vector spaces. Cofree cocommutative coalgebras are defined in a similar way, and can be constructed as the largest cocommu ...

[[Category:Coalgebras]] ...

...ref name="Hinich1998">{{cite journal|last=Hinich |first=Vladimir |title=DG coalgebras as formal stacks|journal = [[Journal of Pure and Applied Algebra]] | volume ...

...ebras''' are a generalization of [[bialgebra]]s that are both algebras and coalgebras but for which the compatibility conditions between the two structures have ...

...can be defined up to [[isomorphism]] as [[initial algebra]]s (resp. final coalgebras) for [[Polynomial functor (type theory)|polynomial functor]]s. In this case ...

...</math>-algebras is equivalently a quasiisomorphism of differential graded coalgebras, and a homotopy between <math>A_\infty</math>-algebra morphisms is equivale ...

...ures in n-Li - Nambu algebras, he introduced the fundamental concepts of 3-coalgebras, 3-algebras and 3-algebras of Hopf. ...