| Autor: |
Abellán García, Fernando, Stern, Walker H. |
| Zdroj: |
Applied Categorical Structures; Dec2022, Vol. 30 Issue 6, p1341-1392, 52p |
| Abstrakt: |
In this paper, we provide a notion of ∞ -bicategories fibred in ∞ -bicategories which we call 2-Cartesian fibrations. Our definition is formulated using the language of marked biscaled simplicial sets: Those are scaled simplicial sets equipped with an additional collection of triangles containing the scaled 2-simplices, which we call lean triangles, in addition to a collection of edges containing all degenerate 1-simplices. We prove the existence of a left proper combinatorial simplicial model category whose fibrant objects are precisely the 2-Cartesian fibrations over a chosen scaled simplicial set S. Over the terminal scaled simplicial set, this provides a new model structure modeling ∞ -bicategories, which we show is Quillen equivalent to Lurie's scaled simplicial set model. We conclude by providing a characterization of 2-Cartesian fibrations over an ∞ -bicategory. This characterization then allows us to identify those 2-Cartesian fibrations arising as the coherent nerve of a fibration of Set Δ + -enriched categories, thus showing that our definition recovers the preexisting notions of fibred 2-categories. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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