I want to define a notion of **cartesian equipment**, the idea being that a [[nlab:bicategory]] $M$ should be a [[nlab:cartesian bicategory]] if and only if the [[nlab:proarrow equipment]] $Map M \to M$ is a cartesian equipment. ### Outline * See [[equipment]] first. With the correct notion of equipment, there are two possible notions of adjoint morphisms, and hence limits: those of [Carboni--Kelly--Verity--Wood](References#ckvw98change), and those of [Grandis--Paré](References#gp99limits) (for double categories). **Question**: Do these notions coincide? Then a cartesian equipment will be an equipment that 'has finite products', that is an equipment $M$ for which the diagonals $M \to M^2$ and $M \to 1$ have right pseudoadjoints.