For formal grammars $𝐴$ and $𝐵$, their tensor $𝐴\otimes 𝐵$ represents the concatenation of the languages they describe. A parse for $𝐴\otimes 𝐵$ at a string $𝑤$ consists of a splitting of $𝑤$ into a prefix $𝑢$ and suffix $𝑣$, along with a parse of $𝑢$ in $𝐴$ and a parse of $𝑣$ in $𝐵$.

Formally, it is defined as:

This operation is exactly the Day convolution of $𝐴$ and $𝐵$, where we view formal grammars as presheaves over the monoid of strings.