Related papers: Homotopy Theory for Ordered Simplicial Complexes

This work develops a comprehensive algebraic model for rational stable parametrized homotopy theory over arbitrary base spaces. Building on the simplicial analogue of the foundational framework of May-Sigurdsson for parametrized spectra,…

This article proposes an algorithm that constructs a Sullivan minimal model for any simply connected simplicial set with effective homology and thereby allows one to decide algorithmically whether two simply connected spaces represented by…

For a field $k$ of characteristic $0$, we compare $k$-linear chain complexes, semisimplicial vector spaces, augmented semisimplicial vector spaces, semicubical vector spaces, and arboreal vector spaces through small differential categorical…

An analogous construction of simplicial homotopy group for Kan complex can be applied to saturated complicial sets to give monoids. In this paper, we investigate how the construction of loop spaces of Kan complexes lifts to the complicial…

An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is…

Let $R$ be a left-Gorenstein ring. We show that there is a Quillen equivalence between singular contraderived model category and singular coderived model category. Consequently, an equivalence between the homotopy category of exact…

A simplicial complex is a set equipped with a down-closed family of distinguished finite subsets. This structure, usually viewed as codifying a triangulated space, is used here directly, to describe "spaces" whose geometric realisation can…

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…

We extend Schwede's work on the unstable global homotopy theory of orthogonal spaces and $\mathcal{L}$-spaces to the category of $*$-modules (i.e., unstable $S$-modules). We prove a theorem which transports model structures and their…

We introduce a model structure on the category of graphs, which is Quillen equivalent to the category of $\mathbb{Z}_2$-spaces. A weak equivalence is a graph homomorphism which induces a $\mathbb{Z}_2$-homotopy equivalence between their box…

We define the notion of a multi-sorted algebraic theory, which is a generalization of an algebraic theory in which the objects are of different "sorts." We prove a rigidification result for simplicial algebras over these theories, showing…

We prove that for certain monoidal (Quillen) model categories, the category of comonoids therein also admits a model structure.

We give a new construction of the model structure on the category of simplicial sets for homotopy $n$-types, originally due to Elvira-Donazar and Hernandez-Paricio, using a right transfer along the coskeleton functor. We observe that an…

We identify the obstructions for the functoriality and the uniqueness of the totalization functor, (partially) defined on the category of simplicial objects in the homotopy category of a stable model category, and we use a result from the…

We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category $\F$ such that the homotopy category of this model structure is equivalent to the stable category $\underline{\F}$ as triangulated…

Given a diagram of rings, one may consider the category of modules over them. We are interested in the homotopy theory of categories of this type: given a suitable diagram of model categories M(s) (as s runs through the diagram), we…

In this paper an algebraic model for unbased rational homotopy theory from the perspective of curved Lie algebras is constructed. As part of this construction a model structure for the category of pseudo-compact curved Lie algebras with…

In this paper we construct new categorical models for the identity types of Martin-L\"of type theory, in the categories Top of topological spaces and SSet of simplicial sets. We do so building on earlier work of Awodey and Warren, which has…

This note extends Quillen's Theorem A to a large class of categories internal to topological spaces. This allows us to show that under a mild condition a fully faithful and essentially surjective functor between such topological categories…

An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is…