Related papers: Cyclic Segal Spaces

We determine the large scale geometry of the minimal displacement set of a hyperbolic isometry of a systolic complex. As a consequence, we describe the centraliser of such an isometry in a systolic group. Using these results, we construct a…

This paper gives an explicit description of the categorical operad whose algebras are precisely symmetric monoidal categories. This allows us to place the operad in a sequence of four, and therefore a sequence of four successively stricter…

Collective Adaptive Systems often consist of many heterogeneous components typically organised in groups. These entities interact with each other by adapting their behaviour to pursue individual or collective goals. In these systems, the…

We start by introducing the basics of configurations of points and lines, and then move into discussing symmetry groups of these configurations. Specifically, we explore how we might classify the symmetries of $(9_3)$ and $(10_3)$ geometric…

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 the concept of cyclicity degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be cyclic. Explicit formulas are obtained for some particular classes of finite groups. An…

We introduce a concept of an embedding of a quadratic space in an associative algebra. The general properties of such embeddings are analyzed by linking it to the Clifford algebra. Conversely, there isa simple description of the standard…

We implement a novel representation of model search spaces as diagrams over a category of models, where we have restricted attention to a broad class of models whose structure is presented by \C-sets. (Co)limits in these diagram categories…

The complexity of biological systems, and the increasingly large amount of associated experimental data, necessitates that we develop mathematical models to further our understanding of these systems. As biological systems are generally not…

This paper introduces a class of linear programming examples which cause the simplex method to cycle indefinitely and which are the simplest possible examples showing this behaviour. The structure of examples from this class repeats after…

Written to be contributed as the "mathematical modeling" chapter of a book, edited by Elaine Landry, to be titled "Categories for the Working Philosopher". In this chapter, category theory is presented as a mathematical modeling framework…

This is the same version that was previously only on my home page. We give a description of geometric realization which makes it evident that it commutes with products. A similar approach is used to treat cyclic sets. Our approach is…

In this document, we develop a new model for the category of dg-categories. Following Rezk's example in the case of classic Segal spaces, we define dg-Segal spaces: functors between free dg-categories of finite type and simplicial spaces to…

We study the minimal dimension of the classifying space of the family of virtually cyclic subgroups of a discrete group. We give a complete answer for instance if the group is virtually poly-Z, word-hyperbolic or countable locally virtually…

The lambda calculus with constructors is an extension of the lambda calculus with variadic constructors. It decomposes the pattern-matching a la ML into a case analysis on constants and a commutation rule between case and application…

We give a $q$-enumeration of circular Dyck paths, which is a superset of the classical Dyck paths enumerated by the Catalan numbers. These objects have recently been studied by Alexandersson and Panova. Furthermore, we show that this…

We investigate the problem of defining group or loop structures on spheres, where by ''sphere'' we mean the level set q(x) = c of a general K-valued quadratic form q, for an invertible scalar c. When K is a field and q non-degenerate, then…

We construct configuration spaces for cyclic covers of the projective line that admit extra automorphisms and we describe the locus of curves with given automorphism group. As an application we provide examples of arbitrary high genus that…

We give a new description of Rosenthal's generalized homotopy fixed point spaces as homotopy limits over the orbit category. This is achieved using a simple categorical model for classifying spaces with respect to families of subgroups.

Given a small category $I$ and a closed symmetric monoidal category $\mm$, we show that the diagram category $\mm^I$ with the objectwise product is a closed symmetric monoidal category. We then prove that if $I$ is a Reedy category and…