
TL;DR
This paper provides a direct proof of Sweedler's description of the cofree cocommutative coalgebra over a vector space, using local cohomology and residues to construct explicit liftings of maps into this universal coalgebra.
Contribution
It offers a new, explicit construction of the cofree cocommutative coalgebra and a direct proof of Sweedler's result utilizing local cohomology techniques.
Findings
Explicit construction of liftings into the cofree coalgebra
A direct proof of Sweedler's description
Application of local cohomology and residues
Abstract
We give a direct proof of a result of Sweedler describing the cofree cocommutative coalgebra over a vector space, and use our approach to give an explicit construction of liftings of maps into this universal coalgebra. The basic ingredients in our approach are local cohomology and residues.
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