Is there a notion of fibered category with box products? By this I roughly mean a fibration $C\rightarrow B$ where $B$ has finite products, along with functors $$\boxtimes: C(X)\times C(Y)\rightarrow C(X\times Y)$$ and some coherent isomorphisms, for example:

$$(f\times g)^* (M\boxtimes N) \leftrightarrow (f^* M) \boxtimes (g^* N)$$ and $$(M\boxtimes N)\boxtimes L \leftrightarrow M\boxtimes (N \boxtimes L) $$

This situation occurs often in geometry, for example:

B=Varieties, C=quasi coherent sheaves, D-modules