The coalgebra structure of the cohomology of multiplicative fibrations

Let p be an odd prime. Let X be a simply connected H-space and let K be a generalized Eilenberg–MacLane space. Let X ˜ be the fibre space induced from an H-map f : X → K . Then X ˜ inherits an H-structure and there is a multiplicative fibration Ω K X ˜ X . The cohomology ring H ⁎ ( X ˜ ; Z p ) is computed in Lin (2009) [4]. In this note, we examine the coalgebra structure of H ⁎ ( X ˜ ; Z p ) . We prove there is a choice of algebra generators for H ⁎ ( X ˜ ; Z p ) with reduced coproduct in im ρ ⁎ ⊗ im ρ ⁎ .