Giora Dula, Peter Hilton, "On Pierce-like idempotents and Hopf invariants", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 583146, 18 pages, 2003. https://doi.org/10.1155/S016117120330331X
On Pierce-like idempotents and Hopf invariants
Given a set with cardinality , a wedge decomposition of a space indexed by , and a cogroup , the homotopy group is shown, by using Pierce-like idempotents, to have a direct sum decomposition indexed by which is strictly functorial if is abelian. Given a class , there is a Hopf invariant on which extends Hopf's definition when is a comultiplication. Then is a functorial sum of over , . Each is a functorial composition of four functors, the first depending only on , the second only on , the third only on , and the fourth only on . There is a connection here with Selick and Walker's work, and with the Hilton matrix calculus, as described by Bokor (1991).
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