Related papers: Fibered Categories a la Jean Benabou
We introduce fibred type-theoretic fibration categories which are fibred categories between categorical models of Martin-L\"{o}f type theory. Fibred type-theoretic fibration categories give a categorical description of logical predicates…
In this paper we start by pointing out that Yoneda's notion of a regular span $S \colon \mathcal{X} \to \mathcal{A} \times \mathcal{B}$ can be interpreted as a special kind of morphism, that we call fiberwise opfibration, in the 2-category…
Given a fibration in groupoids d : D -> I, we define a fibered multicategory as a particular functor p : M -> I, where M has the same objects as D, and its arrows a : X -> Y should be thought of as families of arrows in the multicategory,…
In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…
Jacobs has proposed definitions for (weak, strong, split) generic objects for a fibered category; building on his definition of (split) generic objects, Jacobs develops a menagerie of important fibrational structures with applications to…
We give an elementary exposition of some fundamental facts about fibered (or rather opfibered) categories, in terms of monads and 2-categories. The account avoids any mention of category-valued functors and pseudofunctors.
We define and study notions of comprehension in $(\infty,1)$-category theory. In essence, we do so by implementing B\'{e}nabou's foundations of naive category theory in a univalent meta-theory. In particular, we develop natural…
This is an introduction to Grothendieck's descent theory, with some stress on the general machinery of fibered categories and stacks.
Layered monoidal theories provide a categorical framework for studying scientific theories at different levels of abstraction, via string diagrammatic algebra. We introduce models for three closely related classes of layered monoidal…
Since the seminal work of Ambrosetti and Prodi, the study of global folds was enriched by geometric concepts and extensions accomodating new examples. We present the advantages of considering fibers, a construction dating to Berger and…
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,…
Given a category fibered in groupoids over schemes with a log structure, one produces a category fibered in groupoids over log schemes. We classify the groupoid fibrations over log schemes that arise in this manner in terms of a categorical…
For a large class of geometric objects, the passage to categories of quasi-coherent sheaves provides an embedding in the 2-category of abelian tensor categories. The notion of weakly Tannakian categories introduced by the author gives a…
We prove the well-definedness of some deformations of the fibred biset category in characteristic zero. The method is to realize the fibred biset category and the deformations as the invariant parts of some categories whose compositions are…
These notes were originally developed as lecture notes for a category theory course. They should be well-suited to anyone that wants to learn category theory from scratch and has a scientific mind. There is no need to know advanced…
Latent fibrations are an adaptation, appropriate for categories of partial maps (as presented by restriction categories), of the usual notion of fibration. The paper initiates the development of the basic theory of latent fibrations and…
These are expanded lecture notes from lectures given at the Workshop on higher structures at MATRIX Melbourne. These notes give an introduction to Feynman categories and their applications. Feynman categories give a universal categorical…
We give structural results about bifibrations of (internal) $(\infty,1)$-categories with internal sums. This includes a higher version of Moens' Theorem, characterizing cartesian bifibrations with extensive aka stable and disjoint internal…
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…
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.