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We prove a K\"unneth-type equivalence of derived categories of lisse andconstructible Weil sheaves on schemes in characteristic $p > 0$ for variouscoefficients, including finite discrete rings, algebraic field extensions $E\supset \mathbf Q_\ell$, $\ell \ne p$ and their rings of integers $O_E$. Wealso consider a variant for ind-construtible sheaves which applies to thecohomology of moduli stacks of shtukas over global function fields.

A categorical K\"unneth formula for constructible Weil sheaves