Takeuchi’s Free Hopf Algebra Construction Revisited
نویسنده
چکیده
Takeuchi’s famous free Hopf algebra construction is analyzed from a categorical point of view, and so is the construction of the Hopf envelope of a bialgebra. Both constructions this way appear as compositions of well known and natural constructions. This way certain partially wrong perceptions of these constructions are clarified and their mutual relation is made precise. The construction of Hopf envelopes finally is shown to provide a construction of a Hopf coreflection of bialgebras by simple dualization. The results provided hold for any commutative von Neumann regular ring, not only for fields.
منابع مشابه
Limits and Colimits of Hopf Algebras
It is shown that for any commutative unital ring R the category HopfR of R–Hopf algebras is locally presentable and a coreflective subcategory of the category BialgR of R–bialgebras, admitting cofree Hopf algebras over arbitrary R–algebras. The proofs are based on an explicit analysis of the construction of colimits of Hopf algebras, which generalizes an observation of Takeuchi. Essentially be ...
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