We formalize an abstraction of Grothendieck's philosophy of motives and construct a category of derived motivic spectra in the Segal category $\mathbb{ R} \underline{ \text{ Hom}} ((\text{ dSt}_k)^{ \text{ op}}_{ /F}, \text{ Top})$ ($\text{ dSt}_k$ the Segal category of derived stacks on s$k$-Alg, Top = $L \text{ Set}_{ \Delta}$ the Segal category of simplicial sets), thereby providing a starting point for a construction of a stable motivic homotopy category in the Segal setting.
Categories: math.AG math.CT