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# Introduction to the Category of Derived Motivic Spectra

Mar 2023

We formalize an abstraction of Grothendieck's philosophy of motives andconstruct 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), therebyproviding a starting point for a construction of a stable motivic homotopycategory in the Segal setting.

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