A universal property of the convolution monoidal structure
For a good base monoidal category V, suppose that A is a small monoidal V-category, that PA is the V-category \([A^{op},V]\) with its convolution monoidal structure [\textit{B. Day}, Lect. Notes Math. 137, 1-38 (1970; Zbl 0203.314)], and that C is a cocomplete monoidal V-category. The main result is that restriction along the Yoneda embedding is an equivalence between the category of cocontinuous monoidal functors from PA to C and the category of monoidal functors from A to C.
scientific article; zbMATH DE number 3975173