Definition 2-limit sketch [efr-40Q5]

A 2-limit sketch is a small 2-category \mathcal {T} equipped with a (small) set of cylinders \Theta . A model of the sketch in \mathbb {C} is a 2-functor \mathcal {T} \to \mathbb {C} which carries each cylinder in \Theta to a limit cylinder. We write the category of models and natural transformations \mathsf {Mod}(\mathcal {T},\mathbb {C}) (leaving the set of cylinders implicit). If \mathbb {C} = \mathsf {Cat}, we write simply \mathsf {Mod}(\mathcal {T}).