Related papers: A note on coCartesian fibrations

We investigate fibrancy conditions in the Thomason model structure on the category of small categories. In particular, we show that the category of weak equivalences of a partial model category is fibrant. Furthermore, we describe…

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…

We will show make two contributions to the theory of effective Kan fibrations, which are a more explicit version of the notion of a Kan fibration, a notion which plays a fundamental role in simplicial homotopy theory. We will show that…

We prove a few cases of a conjecture on the invariance of cohomological support loci under derived equivalence by establishing a concrete connection with the related problem of the invariance of Hodge numbers. We use the main case in order…

Draft version of a paper concerning an interpretation of the conditon (UA) in terms of descent with respect to the fibrations of points.

We define a homotopy relation between arrows of a category with weak equivalences, and give a condition under which the quotient by the homotopy relation yields the homotopy category. In the case of the fibrant-cofibrant objects of a model…

This paper presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative…

We prove that if two knots are concordant, their involutive knot Floer complexes satisfy a certain type of stable equivalence.

We prove fibration theorems \`a la Milnor for differentiable real maps with non isolated critical values. We study the situation for maps with linear discriminant, and prove that the concept of d-regularity is the key point for the…

Let X be a compact hyperk\"ahler manifold containing a complex torus L as a Lagrangian subvariety. Beauville posed the question whether X admits a Lagrangian fibration with fibre L. We show that this is indeed the case if X is not…

In order to deduce the internal version of the Brown exact sequence from the internal version of the Gabriel-Zisman exact sequence, we characterize fibrations and $\ast$-fibrations in the 2-category of internal groupoids in terms of the…

In this paper, we prove that certain spherical fibrations over certain CW-complexes are stably fibre homotopy equivalent to $\mm{TOP}$-spherical fibrations (see Definition 1,1). Applying this result, we get a sufficient condition for…

When f : R power n to R power p, is a surjective real analytic map with isolated critical value, we prove that the (m)-regularity condition (in a sense we define) ensures that f ||f|| is a fibration on small spheres, f induces a fibration…

The homotopy category of a model structure on a weakly idempotent complete additive category is proved to be equivalent to the additive quotient of the category of cofibrant-fibrant objects with respect to the subcategory of…

The familiar construction of categories of fractions, due to Gabriel and Zisman, allows one to invert a class W of arrows in a category in a universal way. Similarly, bicategories of fractions allow one to invert a collection of arrows in a…

Let $C_\bullet$ be a simplicial object in the category $Cat$ of small categories. For a field $k$, taking the Grothendieck groups of isomorphism classes of $kC_n$-modules gives rise to a cochain complex, whose cohomology, which we refer to…

Given a symplectic manifold M, we consider a category with objects finite ordered families of Lagrangian submanifolds of M (subject to certain additional constraints) and with morphisms Lagrangian cobordisms relating them. We construct a…

Let $\mathscr{C}$ be an extriangulated category with enough projectives and injectives. We give the definitions of Wakamatsu-tilting subcategories and Wakamatsu-cotilting subcategories of $\mathscr{C}$ and show that they coincide with each…

We introduce maximal and average coherence on lattices by analogy with these notions on frames in Euclidean spaces. Lattices with low coherence can be of interest in signal processing, whereas lattices with high orthogonality defect are of…

We prove a correspondence between $\kappa$-small fibrations in simplicial presheaf categories equipped with the injective or projective model structure (and left Bousfield localizations thereof) and relatively $\kappa$-compact maps in their…