Related papers: Constellations with range and IS-categories
We prove several results in the theory of fusion categories using the product (norm) and sum (trace) of Galois conjugates of formal codegrees. First, we prove that finitely-many fusion categories exist up to equivalence whose global…
In the category of monoids we characterize monomorphisms that are normal, in an appropriate sense, to internal reflexive relations, preorders or equivalence relations. The zero-classes of such internal relations are first described in terms…
Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…
A specialization semilattice is a semilattice together with a coarser preorder satisfying a compatibility condition. We show that the category of specialization semilattices is isomorphic to the category of semilattices with a congruence,…
We show that Compact Groups of Galaxies (CGs) are frequently associated with larger-scale structures, and such associations become more frequent for CGs selected by the same criteria at higher redshifts. Our findings suggest that CGs are an…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
One of the main obstacle to study compactness in topological spaces via ideals was the definition of ideal convergence of subsequences as in the existing literature according to which subsequence of an ideal convergent sequence may fail to…
A family of cosmological models is considered which in a certain synchronized system of reference possess flat slices t = const. They are generated from the Einstein-de Sitter universe by a suitable transformation. Under physically…
We describe a framework for encoding cluster combinatorics using categorical methods. We give a definition of an abstract cluster structure, which captures the essence of cluster mutation at a tropical level and show that cluster algebras,…
Star clusters are ideal tracers of star formation activity in systems outside the volume that can be studied using individual, resolved stars. These unresolved clusters span orders of magnitude in brightness and mass, and their formation is…
This paper investigates a novel structure of stratified L-convex groups, defined as groups possessing stratified L-convex structures, in which the group operations are L-convexity-preserving mappings. It is verified that stratified L-convex…
When a detailed model of a stellar population is unavailable, it is most common to assume that stellar masses are independently and identically distributed according to some distribution: the universal initial mass function (IMF). However,…
Not all the light in galaxy groups and clusters comes from stars that are bound to galaxies. A significant fraction of it constitutes the so-called intracluster or diffuse light (ICL), a low surface brightness component of groups/clusters…
Cyclic poset are generalizations of cyclically ordered sets. In this paper we show that any cyclic poset gives rise to a Frobenius category over any discrete valuation ring R. The continuous cluster categories of arXiv:1209.1879 are…
An $\infty$-cosmos is a setting in which to develop the formal category theory of $(\infty,1)$-categories. In this paper, we explore a few atypical examples of $\infty$-cosmoi whose objects are 2-categories or bicategories rather than…
Restriction categories were established to handle maps that are partially defined with respect to composition. Tensor topology realises that monoidal categories have an intrinsic notion of space, and deals with objects and maps that are…
Expansion of the categorical point of view on many areas of the mathematics and mathematical physics will cause to deeper understanding of genuine features of these problems. New applications of categorical methods are connected with new…
The data of a physical experiment can be represented as a presheaf of probability distributions. A striking feature of quantum theory is that those probability distributions obtained in quantum mechanical experiments do not always admit a…
The categoricity spectrum of a class of structures is the collection of cardinals in which the class has a single model up to isomorphism. Assuming that cardinal exponentiation is injective (a weakening of the generalized continuum…
Right triangulated categories can be thought of as triangulated categories whose shift functor is not an equivalence. We give intrinsic characterisations of when such categories have a natural extriangulated structure and are appearing as…