The McCord Model for the Tensor Product of a Space and a Commutative Ring Spectrum

We begin this paper by noting that, in a 1969 paper in the Transactions, M.C. McCord introduced a construction that can be interpreted as a model for the categorical tensor product of a based space and a topological abelian group. This can be adapted to Segal’s very special Γ-spaces - indeed this is roughly what Segal did — and then to a more modern situation:K ⊗ RwhereKis a based space andRis a unital, augmented, commutative, associative S-algebra.