On Phantom Maps into co-H-spaces

We study the existence of essential phantom maps into co-H-spaces, motivated by Iriye's observation that every suspension space $Y$ of finite type with $H_i(Y;\QQ)\neq 0$ for some $i>1$ is the target of essential phantom maps. We show that Iriye's observation can be extended to the collection of nilpotent, finite type co-H-spaces. This work hinges on an enhanced understanding of the connections between homotopy decompositions of looped co-H-spaces and coalgebra decompositions of tensor algebras due to Grbi\`{c}, Theriault, and Wu.