Related papers: Directed homotopy modules
We work over an arbitrary ring R. Given two truncated projective resolutions of equal length for the same module we consider their underlying chain complexes. We show they may be stabilized by projective modules to obtain a pair of…
Modern categories of spectra such as that of Elmendorf et al equipped with strictly symmetric monoidal smash products allows the introduction of symmetric monoids providing a new way to study highly coherent commutative ring spectra. These…
We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, mapping spaces of algebras over a monad in an appropriate…
Using contact homology, we reobtain some recent results of Geiges and Gonzalo about the fundamental group of the space of contact structures on some 3-manifolds. We show that our techniques can be used to study higher dimensional contact…
We prove analogues of classical results for higher homotopy groups and singular homology groups of pseudotopological spaces. Pseudotopological spaces are a generalization of (\v{C}ech) closure spaces which are in turn a generalization of…
It is now very known how the subprojectivity of modules provides a fruitful new unified framework of the classical projectivity and flatness. In this paper, we extend this fact to the category of complexes by generalizing and unifying…
The polytope subalgebra of deformations of a zonotope can be endowed with the structure of a module over the Tits algebra of the corresponding hyperplane arrangement. We explore this construction and find relations between statistics on…
We introduce constructible directed complexes, a combinatorial presentation of higher categories inspired by constructible complexes in poset topology. Constructible directed complexes with a greatest element, called atoms, encompass common…
In this paper we introduce a path complex that can be regarded as a generalization of the notion of a simplicial complex. The main motivation for considering path complexes comes from directed graphs(digraphs). We obtain a new notion of the…
We introduce a new approach to constructing derived deformation groupoids, by considering them as parameter spaces for strong homotopy bialgebras. This allows them to be constructed for all classical deformation problems, such as…
We study modules over the ring $\widetilde{\C}$ of complex generalized numbers from a topological point of view, introducing the notions of $\widetilde{\C}$-linear topology and locally convex $\widetilde{\C}$-linear topology. In this…
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
We show that the category of log homotopy types is a full subcategory of a category of homotopy types with modulus.
In this paper, a new general decomposition theory inspired from modular graph decomposition is presented. Our main result shows that, within this general theory, most of the nice algorithmic tools developed for modular decomposition are…
In the directed setting, the spaces of directed paths between fixed initial and terminal points are the defining feature for distinguishing different directed spaces. The simplest case is when the space of directed paths is homotopy…
For a Kan complex with a vertex, we have the notion of its simplicial homotopy groups. In this paper, for a weak complicial set in the sense of Verity with a vertex, we construct monoids which are a generalization of simplicial homotopy…
The field of directed type theory seeks to design type theories capable of reasoning synthetically about (higher) categories, by generalizing the symmetric identity types of Martin-L\"of Type Theory to asymmetric hom-types. We articulate…
A groupoid is a small category in which each morphism has an inverse. A topological groupoid is a groupoid in which both sets of objects and morphisms have topologies such that all groupoid structure maps are continuous. The notion of…
This paper studies the existence of model category structures on algebras and modules over operads in monoidal model categories.