Homomorphisms of homotopy coalgebras (Q818354)

The concept of higher order homotopy coalgebra was introduced by Arkowitz and Golasinski. The authors consider a special case of it to define \(WHC_k\)-spaces and \(HC_k\)-spaces as collections of spaces between co-\(H\)-spaces and suspensions, which dualizes Stasheff's theory of \(A_k\)-spaces. By definition, \(WHC_k\)-spaces can be considered as the duals of \(A_{k+1}\)-spaces, and we have coprojective \(r\)-spaces \(C_r(X)\) \((1\leq r \leq k+1)\) for any \(WHC_k\)-space \(X\). The authors also extend the Berstein-Hilton theorems which deal with the primitive homotopy type of a suspension and the class of a suspension map.