Related papers: The universal coCartesian fibration
We prove properness of (co)Cartesian fibrations as well as a straightening and unstraightening equivalence, which is compatible with cartesian products, when the base is the nerve of a small category.
The straightening-unstraightening correspondence of Grothendieck--Lurie provides an equivalence between cocartesian fibrations between $(\infty, 1)$-categories and diagrams of $(\infty, 1)$-categories. We provide an alternative proof of…
We provide a short and reasonably self-contained proof of Lurie's straightening equivalence, relating cartesian fibrations over a given $\infty$-category $S$ with contravariant functors from $S$ to the $\infty$-category of small…
We define and study cartesian and cocartesian fibrations between categories internal to an $\infty$-topos and prove a straightening equivalence in this context.
The unstraightening construction due to Lurie establishes an equivalence between presheaves and fibrations, using one prominent model of $(\infty,1)$-categories, namely quasi-categories. In this work we generalize this result by proving…
We give a complete proof of the fact that a contact structure that is sufficiently close to a Reebless foliation is universally tight.
In this paper, we propose a generalization of a congruence due to Carlitz.
We review the concept of a univalent fibration and show by elementary means that every Kan fibration in simplicial sets can be embedded in a univalent Kan fibration.
We give a simple diagrammatic proof of the Frobenius property for generic fibrations, that does not depend on any additional structure on the interval object such as connections.
We use the complete Segal approach to the theory of Cartesian fibrations to define and study representable Cartesian fibrations, generalizing representable right fibrations which have played a key role in $\infty$-category theory. In…
By measuring or calculating coalescence times for several models of coalescence or evolution, with and without selection, we show that the ratios of these coalescence times become universal in the large size limit and we identify a few…
We formulate a model-independent theory of co/cartesian morphisms and co/cartesian fibrations: that is, one which resides entirely *within the $\infty$-category of $\infty$-categories*. We prove this is suitably compatible with the…
For every fibration $f : X \to B$ with $X$ a compact K\"ahler manifold, $B$ a smooth projective curve, and a general fiber of $f$ an abelian variety, we prove that $f$ has an algebraic approximation.
We give a direct proof of the fact that Lurie's Unstraightening functor induces an equivalence between the strict $(\infty,2)$-category of indexed quasi-categories and the strict $(\infty,2)$-category of fibered quasi-categories over any…
In this paper, we study equivariant Hurewicz fibrations, obtain their internal characteristics, and prove theorems on relationship between equivariant fibrations and fibrations generated by them. Local and global properties of equivariant…
We prove a universal property for $\infty$-categories of spans in the generality of Barwick's adequate triples, explicitly describe the cocartesian fibration corresponding to the span functor, and show that the latter restricts to a…
We prove finiteness of hyperkaehler Lagrangian fibrations in any fixed dimension with fixed Fujiki constant and discriminant of the Beauville-Bogomolov-Fujiki lattice, up to deformation. We also prove finiteness of hyperk\"ahler Lagrangian…
We develop a categorical framework for reasoning about abstract properties of differentiation, based on the theory of fibrations. Our work encompasses the first-order fragments of several existing categorical structures for differentiation,…
We study the behavior of irregular fibrations of a variety under derived equivalence of its bounded derived category. In particular we prove the derived invariance of the existence of an irregular fibration over a variety of general type,…
We give effective bounds for the uniformity of the Iitaka fibration. These bounds follow from an effective theorem on the birationality of some adjoint linear series. In particular we derive an effective version of the main theorem in [17].