Related papers: Double Fibrations

Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.

We give a rather general construction of double categories and so, under further conditions, double groupoids, from a structure we call a `double module'. We also give a homotopical construction of a double groupoid from a triad consisting…

Kodaira fibrations are surfaces of general type with a non-isotrivial fibration, which are differentiable fibre bundles. They are known to have positive signature divisible by $4$. Examples are known only with signature 16 and more. We…

We define the notion of Cartesian 2-fibrations, and prove a weak analogue of straightening. Using Barwick's notion of operator categories and the notion of a Cartesian 2-fibration, we extend the notion of $\infty$-operads to the…

In this paper we introduce the notion of Hurewicz fibrations in the class of embedding maps of orbifold charts by giving the concept of E-fibration embedding. We study the fundamental properties of this concept such as the restriction,…

We describe the construction of the slice fibration of a given one.

In this work we propose a realization of Lurie's prediction that inner fibrations $p: X \rightarrow A$ are classified by $A$-indexed diagrams in a ``higher category" whose objects are $\infty$-categories, morphisms are correspondences…

Let $X \to S$ be a minimal abelian fibration of relative dimension $n$ over a curve. We classify all possible singular fibers $X_s$ having $(n-1)$-dimensional ``abelian variety parts''. This generalizes Kodaira's work on elliptic…

In this paper we introduce and investigate the notions of diagrams and discrete extensions in the study of finitary $2$-representations of finitary $2$-categories.

The aim of this paper is to generalize Grothendieck's theory of smooth functors in order to include within this framework the theory of fibered categories. We obtain in particular a new characterization of fibered categories.

We use double categories to obtain a single theorem characterizing certain exponentiable morphisms of small categories, topological spaces, locales, and posets.

A 2-categorical generalisation of elementary topos is provided and some of the properties of the yoneda structure it generates are explored. Examples relevant to the globular approach to higher category theory are discussed. This paper also…

In this paper we prove birational rigidity of large classes of Fano-Mori fibre spaces over a base of arbitrary dimension, bounded from above by a constant that depends on the dimension of the fibre only. In order to do that, we first show…

We introduce a method to lift monads on the base category of a fibration to its total category. This method, which we call codensity lifting, is applicable to various fibrations which were not supported by its precursor, categorical…

We construct in a unifying way skew-multicategories and multicategories of double and Gray-categories that we call Gray (skew) multicategories. We study their different versions depending on the types of functors and higher transforms. We…

Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explicit description of the information required to define any…

This is a survey of history, methods and developments in the theory of cycle spaces of flag domains, and new results on double fibration transforms and their applications.

We develop the quadratic technique of proving birational rigidity of Fano-Mori fibre spaces over a higher-dimensional base. As an application, we prove birational rigidity of generic fibrations into Fano double spaces of dimension…

We define a new model structure on the category of small categories, which is intimately related to the notion of coverings and fundamental groups of small categories. Fibrant objects in the model structure coincide with groupoids, and the…

Dimitri Ara's 2-quasi-categories, which are certain presheaves over Andr\'{e} Joyal's 2-cell category $\Theta_2$, are an example of a concrete model that realises the abstract notion of $(\infty,2)$-category. In this paper, we prove that…