Related papers: A characterization of final functors between inter…
The main result concerns a bicategorical factorization system on the bicategory $\mathrm{Cat}$ of categories and functors. Each functor $A\xra{f} B$ factors up to isomorphism as $A\xra{j}E\xra{p}B$ where $j$ is what we call an ultimate…
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…
We introduce and discuss the notion of naturally full functor. The definition is similar to the definition of separable functor: a naturally full functor is a functorial version of a full functor, while a separable functor is a functorial…
In this paper, we state and prove precise theorems on the classification of the category of (braided) categorical groups and their (braided) monoidal functors, and some applications obtained from the basic studies on monoidal functors…
In this note we prove that distributors between groupoids in a Barr-exact category E form the bicategory of relations relative to the comprehensive factorization system in Gpd(E). Revised version.
Internal categories feature notions of limit and completeness, as originally proposed in the context of the effective topos. This paper sets out the theory of internal completeness in a general context, spelling out the details of the…
A $\mathcal{C}$-set is a functor from the category $\mathcal{C}$ to the category of finite sets and functions. The category of $\mathcal{C}$-sets, $\mathcal{C} - \operatorname*{set}$, is defined as the category whose objects are…
A simple criterion for a functor to be finitary is presented: we call $F$ finitely bounded if for all objects $X$ every finitely generated subobject of $FX$ factorizes through the $F$-image of a finitely generated subobject of $X$. This is…
We give a geometric characterization of finite rational groups. In particular, we prove that a finite group is rational if and only if there exists a finite geometry $\Gamma$ of type $I$ and action of $G$ on $\Gamma$ as a group of…
For a category B with finite products, we first characterize pseudofunctors from B to Cat whose corresponding opfibration is cartesian monoidal. Among those, we then characterize the ones which extend to pseudofunctors from internal groups…
An answer to the question investigated in this paper brings a new characterization of internal groupoids such that: (a) it holds even when finite limits are not assumed to exist; (b) it is a full subcategory of the category of…
We prove that every finitary polynomial endofunctor of a category $C$ has a final coalgebra if $C$ is locally Cartesian closed, has finite disjoint coproducts and a natural number object. More generally, we prove that the category of…
We give a natural notion of (non-exact) integral functor in the context of k-linear and graded categories. In this broader sense, we prove that every k-linear and graded functor is integral.
The paper studies analytic functors between presheaf categories. Generalising results of A. Joyal and of R. Hasegawa for analytic endofunctors on the category of sets, we give two characterisations of analytic functors between presheaf…
We prove that certain Fuchsian triangle groups are profinitely rigid in the absolute sense, i.e. each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. We also develop a method…
Graduated locally finitely presentable categories are introduced, examples include categories of sets, vector spaces, posets, presheaves and Boolean algebras. A finitary functor between graduated locally finitely presentable categories is…
A locally compact groupoid is said to be exact if its associated reduced crossed product functor is exact. In this paper, we establish some permanence properties of exactness, including generalizations of some known results for exact…
We prove that an algebraic group over a field $k$is affine precisely when its Picard group is torsion, and show that in this case the Picard group is finite when $k$ is perfect, and the product of a finite group of order prime to $p$ and a…
We prove that a group $G$ is locally finite if and only if every surjective real (or complex) linear cellular automaton with finite-dimensional alphabet over $G$ is injective.
Let $X$ be a set and let $S$ be an inverse semigroup of partial bijections of $X$. Thus, an element of $S$ is a bijection between two subsets of $X$, and the set $S$ is required to be closed under the operations of taking inverses and…