The external product ⊗ ¯ : 𝒱 ^ × 𝒱 ^ → ( 𝒱 × 𝒱 ) ^ : ¯ tensor-product → ^ 𝒱 ^ 𝒱 ^ 𝒱 𝒱 \overline{\otimes}:\widehat{\mathcal{V}}\times\widehat{\mathcal{V}}\to\widehat% {(\mathcal{V}\times\mathcal{V})} of Presheaves on a Monoidal Category 𝒱 𝒱 \mathcal{V} is given by
(P⊗¯Q)(X,Y)=P(X)×Q(Y)𝑃¯tensor-product𝑄𝑋𝑌𝑃𝑋𝑄𝑌(P\overline{\otimes}Q)(X,Y)=P(X)\times Q(Y)