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darij grinberg
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This may be the third time here that I am linking to Michiel Hazewinkel's "Witt vectors, part 1". This time it's Section 12, mainly 12.11. The graded cofree coalgebra over a vector space is the tensor coalgebra (i. e. the tensor algebra, but you forget the tensor multiplication and instead take the deconcatenation coproduct). "Graded" means that all morphisms in the universal property are supposed to be graded. If you leave out the "graded", however, things get difficult. I have but briefly skimmed the contents of this paperthis paper (Michiel Hazewinkel, Cofree coalgebras and multivariable recursiveness, Journal of Pure and Applied Algebra, Volume 183, Issues 1--3, 1 September 2003, Pages 61-103), but it seems to contain a description.

This may be the third time here that I am linking to Michiel Hazewinkel's "Witt vectors, part 1". This time it's Section 12, mainly 12.11. The graded cofree coalgebra over a vector space is the tensor coalgebra (i. e. the tensor algebra, but you forget the tensor multiplication and instead take the deconcatenation coproduct). "Graded" means that all morphisms in the universal property are supposed to be graded. If you leave out the "graded", however, things get difficult. I have but briefly skimmed the contents of this paper, but it seems to contain a description.

This may be the third time here that I am linking to Michiel Hazewinkel's "Witt vectors, part 1". This time it's Section 12, mainly 12.11. The graded cofree coalgebra over a vector space is the tensor coalgebra (i. e. the tensor algebra, but you forget the tensor multiplication and instead take the deconcatenation coproduct). "Graded" means that all morphisms in the universal property are supposed to be graded. If you leave out the "graded", however, things get difficult. I have but briefly skimmed the contents of this paper (Michiel Hazewinkel, Cofree coalgebras and multivariable recursiveness, Journal of Pure and Applied Algebra, Volume 183, Issues 1--3, 1 September 2003, Pages 61-103), but it seems to contain a description.

Source Link
darij grinberg
  • 33.8k
  • 4
  • 118
  • 253

This may be the third time here that I am linking to Michiel Hazewinkel's "Witt vectors, part 1". This time it's Section 12, mainly 12.11. The graded cofree coalgebra over a vector space is the tensor coalgebra (i. e. the tensor algebra, but you forget the tensor multiplication and instead take the deconcatenation coproduct). "Graded" means that all morphisms in the universal property are supposed to be graded. If you leave out the "graded", however, things get difficult. I have but briefly skimmed the contents of this paper, but it seems to contain a description.