2-Cartesian Fibrations I: A Model for $$\infty $$-Bicategories Fibred in $$\infty $$-Bicategories

In this paper, we provide a notion of $$\infty $$ -bicategories fibred in which call 2-Cartesian fibrations. Our definition is formulated using the language marked biscaled simplicial sets: Those are scaled sets equipped with an additional collection triangles containing 2-simplices, lean triangles, addition to edges all degenerate 1-simplices. We prove existence left proper combinatorial model category whose fibrant objects precisely fibrations over chosen set S. Over terminal set, provides new structure modeling -bicategories, show Quillen equivalent Lurie’s model. conclude by providing characterization -bicategory. This then allows us identify those arising as coherent nerve fibration $${\text {Set}}^+_{\Delta }$$ -enriched categories, thus showing that our recovers preexisting notions 2-categories.