Related papers: Limits and colimits of crossed groups
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…
We introduce and investigate generalizations of interval and proper interval graphs to simplicial complexes, including strong interval, unit interval, and under closed variants. Through equivalent combinatorial and algebraic…
Notions of generalized multicategory have been defined in numerous contexts throughout the literature, and include such diverse examples as symmetric multicategories, globular operads, Lawvere theories, and topological spaces. In each case,…
In the space of marked group, we determine the structure of groups which are limit points of the set of all generalized quaternion groups.
In this paper using split extensions of group-groupoids we obtain the notion of crossed modules over group-grouoids which are also called 2-groups and we prove a categorical equivalence of these types of crossed modules and double…
We extend the notion of the nerve of a category for a small class of crossed simplicial groups, explicitly describing them using generators and relations. We do this by first considering a generalised bar construction of a group before…
We introduce and study structured enhancement of the notion of a crossed simplicial group, which we call an operadic crossed simplicial group. We show that with each operadic crossed simplicial group one can associate a certain operad in…
We introduce some algebraic structures such as singularity, commutators and central extension in modified categories of interest. Additionally, we introduce the cat$^{1}$-objects with their connection to crossed modules in these categories…
Let $H$ be a Hopf algebra in braided category $\cal C$. Crossed modules over $H$ are objects with both module and comodule structures satisfying some comatibility condition. Category ${\cal C}^H_H$ of crossed modules is braided and is…
Braided monoidal categories arise naturally as centres of monoidal categories and have been the focus of much recent attention in both mathematics and physics. By suitably restricting the use of the exchange rule, we obtain a sequent…
Bounded cohomology of groups was first studied by Gromov in 1982. Since then it has sparked much research in Geometric Group Theory. However, it is notoriously hard to explicitly compute bounded cohomology, even for most basic…
We develop a Hodge theory for relative simple normal crossing varieties over an Artinian base scheme. We introduce the notion of a mixed Hodge structure over an Artin ring, which axiomatizes the structure that is found on the cohomology of…
We address the (pointed) homotopy of crossed module morphisms in modified categories of interest; which generalizes the groups and various algebraic structures. We prove that, the homotopy relation gives rise to an equivalence relation;…
We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…
Due to the noncommutative nature of quaternions and octonions we introduce barred operators. This objects give the opportunity to manipulate appropriately the hypercomplex fields. The standard problems arising in the definitions of…
Recently, we have endowed various categories of groups with topologies. The purpose of this paper is to introduce on these categories others topologies which are statistically more suitable to study well-known problems in groups theory. We…
We outline the main features of the definitions and applications of crossed complexes and cubical $\omega$-groupoids with connections. These give forms of higher homotopy groupoids, and new views of basic algebraic topology and the…
We show how the framework of crossed simplicial groups may be used to provide a classification of topological field theories on open cobordism categories defined by reductions of the structure group to a planar Lie group. Such theories are…
Transformational musical theory has so far mainly focused on the study of groups acting on musical chords, one of the most famous example being the action of the dihedral group D24 on the set of major and minor chords. Comparatively less…
The title refers to the area of research which studies infinite groups using measure-theoretic tools, and studies the restrictions that group structure imposes on ergodic theory of their actions. The paper is a survey of recent developments…