Related papers: Higher Structures in Homotopy Type Theory
We study 2-monads and their algebras using a Cat-enriched version of Quillen model categories, emphasizing the parallels between the homotopical and 2-categorical points of view. Every 2-category with finite limits and colimits has a…
The homotopy theory of gauge groups has received considerable attention in recent decades. In this work, we study the homotopy theory of gauge groups over some high dimensional manifolds. To be more specific, we study gauge groups of…
We describe a construction of the modular class associated to a representation up to homotopy of a Lie groupoid. In the case of the adjoint representation up to homotopy, this class is the obstruction to the existence of a volume form, in…
This paper is an expository account of the theory of stable infinity categories. We prove that the homotopy category of a stable infinity category is triangulated, and that the collection of stable infinity categories is closed under a…
We construct a Goodwillie tower of categories which interpolates between the category of pointed spaces and the category of spectra. This tower of categories refines the Goodwillie tower of the identity functor in a precise sense. More…
This book is an account of certain topics in general and algebraic topology. Instead of laying out a synopsis of each chapter, here is a sample of some of what is taken up: 1) Nilpotency and its role in homotopy theory. 2) Bousfield's…
We present a new approach to simple homotopy theory of polyhedra using finite topological spaces. We define the concept of collapse of a finite space and prove that this new notion corresponds exactly to the concept of a simplicial…
We use homotopy operators for the $L_\infty$-algebra associated with an equivariant deformation problem in order to describe a smooth parametrization of the space of structures around a given one. Along the way we give new algebraic and…
Many first-order equational theories, such as the theory of groups or boolean algebras, can be presented by a smaller set of axioms than the original one. Recent studies showed that a homological approach to equational theories gives us…
We present different ways of endowing a particular category of graphs with Quillen model structures. We show, among other things, that the core of a graph can be seen as its homotopy type in an appropriate Quillen model structure, and that…
We introduce several highness notions on degrees related to the problem of computing isomorphisms between structures, provided that isomorphisms exist. We consider variants along axes of uniformity, inclusion of negative information, and…
We study the homotopy theory of diagrams of chain complexes over a field indexed by a finite poset, and show that it can be completely described in terms of appropriate diagrams of graded vector spaces.
Homotopy links have proven to be one of the most powerful tools of stratified homotopy theory. In previous work, we described combinatorial models for the generalized homotopy links of a stratified simplicial set. For many purposes, in…
Uniformly finite homology is a coarse invariant for metric spaces; in particular, it is a quasi-isometry invariant for finitely generated groups. In this article, we study uniformly finite homology of finitely generated amenable groups and…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
We produce a class of $\omega$-categorical structures with finite signature by applying a model-theoretic construction -- a refinement of the Hrushosvki-encoding -- to $\omega$-categorical structures in a possibly infinite signature. We…
This paper contains two results on how homotopy limits of topological spaces interact with connectivity. The first is a formula for the connectivity of the homotopy limit of diagrams shaped over suitably finite categories, in terms of the…
Recently there has been growing interest in discrete homotopies and homotopies of graphs beyond treating graphs as 1-dimensional simplicial spaces. One such type of homotopy is $\times$-homotopy. Recent work by Chih-Scull has developed a…
D. K. Biss (Topology and its Applications 124 (2002) 355-371) introduced the topological fundamental group and presented some interesting basic properties of the notion. In this article we intend to extend the above notion to homotopy…
A typoid is a type equipped with an equivalence relation, such that the terms of equivalence between the terms of the type satisfy certain conditions, with respect to a given equivalence relation between them, that generalise the properties…