Related papers: Fibered Categories a la Jean Benabou

Fibring of modal logics is a well-established formalism for combining countable families of modal logics into a single fibred language with common semantics, characterized by fibred models. Inspired by this formalism, fibring of neural…

This survey of some of the more topological aspects of the placement problem for complex curves in complex surfaces was originally published in L'Enseignement Mathematique 29 (1983). The present LaTeXed redaction corrects several…

In 2013, Conway and Ryba wrote a fascinating paper called Fibonometry. The paper, as one might guess, is about the connection between Fibonacci numbers and trigonometry. We were fascinated by this paper and looked at how we could generalize…

We study the existence problem and the enumeration problem for sections of Serre fibrations over compact orientable surfaces. When the fundamental group of the fiber is finite, a complete solution is given in terms of 2-dimensional…

We investigate fibrations by non-hyperelliptic curves of arithmetic genus three and geometric genus one in characteristic two. Assuming that there is only one moving singularity and that its image in the Frobenius pullback of the fibration…

We have developed a methodology for the systematic generation of a large image dataset of macerated wood references, which we used to generate image data for nine hardwood genera. This is the basis for a substantial approach to automate,…

Written to be contributed as the "mathematical modeling" chapter of a book, edited by Elaine Landry, to be titled "Categories for the Working Philosopher". In this chapter, category theory is presented as a mathematical modeling framework…

The derived category of bounded complexes of coherent sheaves is one of the most important algebraic invariants of a smooth projective variety. An important approach to understand derived categories is to construct full strongly exceptional…

We set the foundations of a theory of Grothendieck $(\infty,2)$-topoi based on the notion of fibrational descent, which axiomatizes both the existence of a classifying object for fibrations internal to an $(\infty,2)$-category as well as…

In this paper we generalize Tannakian formalism to fiber functors over general tensor categories. We will show that (under some technical conditions) if the fiber functor has a section, then the source category is equivalent to the category…

The textured images' classification assumes to consider the images in terms of area with the same texture. In uncertain environment, it could be better to take an imprecise decision or to reject the area corresponding to an unlearning…

We define a general mathematical framework for linguistics based on the theory of fibrations, called FibLang. We start by modelling the interaction between linguistics and cognition in the most general way possible, with a heavy focus on…

The concept of a morphism determined by an object provides a method to construct or classify morphisms in a fixed category. We show that this works particularly well for triangulated categories having Serre duality. Another application of…

This habilitation memoir (in French, submitted in May 2014) is made up of five chapters, each being an introduction to work of the author between 2006 and 2014. The core of the memoir consists of the first three chapters, pertaining to…

This is the fourth (and last) prepublication version of a book on derived categories, that will be published by Cambridge University Press. The purpose of the book is to provide solid foundations for the theory of derived categories, and to…

Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. Although it can be treated purely as an algebraic subject, it is inherently topological in nature: the…

In this paper we describe two ways on which cofibred categories give rise to bisimplicial sets. The "fibred nerve" is a natural extension of Segal's classical nerve of a category, and it constitutes an alternative simplicial description of…

This work presents an exposition of both the internal structure of derived category of an abelian category D*(A) and its contribution in solving problems, particularly in algebraic geometry. Calculation of some morphisms will be presented…

This paper studies graded manifolds with local coordinates concentrated in non-negative degrees. We provide a canonical description of these objects in terms of classical geometric data and, building on this geometric viewpoint, we prove…

In these notes we provide the foundation for the deformation theoretic parts of arXiv:0807.3753 and arXiv:math/0102005.