Related papers: Fibered Categories a la Jean Benabou
In this article, we develop a notion of Quillen bifibration which combines the two notions of Grothendieck bifibration and of Quillen model structure. In particular, given a bifibration $p:\mathcal E\to\mathcal B$, we describe when a family…
In this paper we extend the generalized algebraic fundamental group constructed by Esnault and Hogadi to general fibered categories using the language of gerbes. As an application we obtain a Tannakian interpretation for the Nori…
The goal of this paper is to construct a category of motivic "sheaves" on an algebraic variety defined over a subfield of C, using Nori's method. This categoryis abelian and it possesses faithful exact realization functors to the…
Translating notions and results from category theory to the theory of computability models of Longley and Normann, we introduce the Grothendieck computability model and the first-projection-simulation. We prove some basic properties of the…
K. S. S. Nambooripad introduced an interesting class of categories known as normal categories, which are categories with subobjects, morphisms admitting factorization and having sufficiently many cones. These normal categories plays…
These are the lecture notes for a short course on tensor categories. The coverage in these notes is relatively non-technical, focussing on the essential ideas. They are meant to be accessible for beginners, but it is hoped that also some of…
It goes back to Ahlfors that a real algebraic curve admits a real-fibered morphism to the projective line if and only if the real part of the curve disconnects its complex part. Inspired by this result, we are interested in characterising…
In this paper, we study `a fibration of metric spaces' that was originally introduced by Leinster in the study of the magnitude and called metric fibrations. He showed that the magnitude of a metric fibration splits into the product of…
Network representations of systems from various scientific and societal domains are neither completely random nor fully regular, but instead appear to contain recurring structural building blocks. These features tend to be shared by…
We give criteria for the existence of a Serre functor on the derived category of a gauged Landau-Ginzburg model. This is used to provide a general theorem on the existence of an admissible (fractional) Calabi-Yau subcategory of a gauged…
This book provides an inviting tour through sheaf theory, from the perspective of applied category theory and pitched at a less specialized audience than is typical with introductions to sheaves. The book makes it as easy as possible for…
In this paper, we define a generalization of indexed categories and contextual categories which we call contextually indexed (contextual) categories. While contextual categories are models of ordinary type theories, contextually indexed…
A toric variety is called fibered if it can be represented as a total space of fibre bundle over toric base and with toric fiber. Fibered toric varieties form a special case of toric variety bundles. In this note we first give an…
Representations over diagrams of abelian categories unify quite a few notions appearing widely in literature such as representations of categories, presheaves of modules over categories, representations of species, etc. In this series of…
In this brief note we explore the space of genus one and elliptic fibrations within CY manifolds, their organizing principles, and how they relate to the set of all CY manifolds. We provide examples of genus one fibered manifolds that…
Working over imperfect fields, we give a comprehensive classification of genus-one curves that are regular but not geometrically regular, extending the known case of geometrically reduced curves. The description is given intrinsically, in…
For a generalisation of the classical theory of Hopf algebra over fields, A. Brugui\`eres and A. Virelizier study opmonoidal monads on monoidal categories (which they called {\em bimonads}). In a recent joint paper with S. Lack the same…
The original article titled "Vari\'et\'es (non s\'epar\'ees) \`a une dimension et structures feuillet\'ees du plan" was published in 1957 in French in L'Enseignement Math\'ematique. It establishes a beautiful connection between foliations…
Derived categories were invented by Grothendieck and Verdier around 1960, not very long after the "old" homological algebra (of derived functors between abelian categories) was established. This "new" homological algebra, of derived…
Category theory is famous for its innovative way of thinking of concepts by their descriptions, in particular by establishing universal properties. Concepts that can be characterized in a universal way receive a certain quality seal, which…