Related papers: Distributors and the comprehensive factorization s…

Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…

Rig categories with finite biproducts are categories with two monoidal products, where one is a biproduct and the other distributes over it. In this work we present tape diagrams, a sound and complete diagrammatic language for these…

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…

Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce…

We determine all the ways in which a direct product of two finite groups can be expressed as the set-theoretical union of proper subgroups in a family of minimal cardinality.

We study polynomial functors over locally cartesian closed categories. After setting up the basic theory, we show how polynomial functors assemble into a double category, in fact a framed bicategory. We show that the free monad on a…

By restricting to a class of localic open groupoids $G$ which, similarly to Lie groupoids, possess appropriate covers $\widehat G\to G$ by \'etale groupoids, we extend results about groupoid actions and quantales that were previously proved…

We consider finitely presented,residually finite groups $G$ and finitely generated normal subgroups $A$ such that the inclusion $A\hookrightarrow G$ induces an isomorphism from the profinite completion of $A$ to a direct factor of the…

For $X$ a complete, reduced, geometrically connected scheme over a perfect field of characteristic $p>0$, we analyze the decomposition of Nori's fundamental group scheme into its local and \'etale parts and raise the question of the…

We prove existence of equalizers in certain categories of cocomplete cocategories. This allows us to complete the proof of the fact that A-infinity functor categories arise as internal Hom-objects in the category of differential graded…

In the paper we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a…

We consider the category of partial actions, where the group and the set upon which the group acts can vary. Within this framework, we develop a theory of quotient partial actions and prove that this category is both (co)complete and…

We show that extension groups between two polynomial functors on free groups are the same in the category of all functors and in a subcategory of polynomial functors of bounded degree. We give some applications. ---- On montre que les…

In this paper, we present Sch\"utzenberger's factorization in different combinatorial contexts and show that its validity is not restricted to these cases but can be extended to every Lie algebra endowed with an ordered basis. We also…

The main aim of this paper is to present a program on computer for decide if an universal algebra is a groupoid. Using the theory of groupoids and the program BGroidAP1 we prove a theorem of classification for the groupoids of type (4;2).

The Jacobi system on a full-line lattice is considered when it contains additional weight factors. A factorization formula is derived expressing the scattering from such a generalized Jacobi system in terms of the scattering from its…

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.

We give a classification of all quasitriangular structures and ribbon elements of $\mathcal{D}(G)$ explicitly in terms of group homomorphisms and central subgroups. This can equivalently be interpreted as an explicit description of all…

We review the theory of derivators from the ground up, defining new classes of derivators which were originally motivated by derivator K-theory. We prove that many old arguments that relied on homotopical bicompleteness hold also for…

We prove that the $\infty$-category of orthogonal factorization systems embeds fully faithfully into the $\infty$-category of double $\infty$-categories. Moreover, we prove an (un)straightening equivalence for double $\infty$-categories,…