On Sweedler's cofree cocommutative coalgebra

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.

v2: improved some notation and fixed typos. Published in J. Pure and Applied Algebra