Fernando Abellán
In this work we provide a model-independent notion of local fibrations of (∞,2)-categories which generalises the well-known theory of locally coCartesian fibrations of (∞,1)-categories. Based on previous work, we construct a model category which serves as a specific combinatorial model for this type of fibrations. Our main result is a generalisation of the locally coCartesian straightening and unstraightening construction of Lurie. Finally, as an application of our results we provide a version of the Yoneda lemma for (∞,2)-categories.
