We study the categorical structure of the Grothendieck construction of an indexed category \( \mathcal L : \mathcal C^{op} \to \mathbf{CAT} \), starting with the study of fibred limits, colimits, and monoidal structures. Next, we give sufficient conditions for the monoidal closure of the total category \( \Sigma_{\mathcal C}\mathcal L \) of a Grothendieck construction of an indexed category \( \mathcal L : \mathcal C^{op} \to \mathbf{CAT} \). Our analysis is a generalization of Gödel's Dialectica interpretation, and it relies on a novel notion of \( \Sigma \)-tractable monoidal structure. As we will see, \( \Sigma \)-tractable coproducts simultaneously generalize cocartesian coclosed structures, biproducts and extensive coproducts. We analyse when the closed structure is fibred - usually it is not.