Related papers: Simplicial model structures on pro-categories
In the first half of this paper, we outline the construction of a new class of abelian pro-$p$ groups, which covers all countably-based pro-$p$ groups. In the second half, we study them, and classify them up to topological isomorphism and…
We prove that, under certain conditions, the model structure on a monoidal model category $\mathcal{V}$ can be transferred to a model structure on the category of $\mathcal{V}$-enriched coloured (symmetric) operads. As a particular case we…
Locally partial-ordered spaces (local po-spaces) have been used to model concurrent systems. We provide equivalences for these spaces by constructing a model category containing the category of local po-spaces. We show the category of…
We prove the uniqueness, the functoriality and the naturality of cylinder objects and path objects in closed simplicial model categories.
In this paper, we construct an analogy of holonomy of connection to simplicial sets using A-infinity-categories. To construct it, we develop fiberwise integrals on simplicial sets and define an iterated integral on simplicial sets. It is an…
We give a fully constructive proof that there is a proper cartesian $\omega$-combinatorial model structure on the category of simplicial sets, whose generating cofibrations and trivial cofibrations are the usual boundary inclusion and horn…
We put a Quillen model structure on the category of small categories enriched in simplicial $k$-modules and non-negatively graded chain complexes of $k$-modules, where $k$ is a commutative ring. The model structure is obtained by transfer…
We construct a discrete model of the homotopy theory of $S^1$-spaces. We define a category $\sP$ with objects composed of a simplicial set and a cyclic set along with suitable compatibility data. $\sP$ inherits a model structure from the…
The aim of this note is threefold. The first is to obtain a simple characterization of relative constructible sheaves when the parameter space is projective. The second is to study the relative Fourier-Mukai for relative constructible…
In this paper by using the ring of real-valued continuous functions $C(X)$, we prove a theorem in profinite spaces which states that for a compact Hausdorff space $X$, the set of its connected components $X/_{\sim}$ endowed with some…
We show that if $(M,\tensor,I)$ is a monoidal model category then $\REnd_M(I)$ is a (weak) 2-monoid in $\sSet$. This applies in particular when $M$ is the category of $A$-bimodules over a simplicial monoid $A$: the derived endomorphisms of…
This paper is part of a series of three articles with the objective of investigating a stratified version of the homotopy hypothesis in terms of semi-model structures that interact well with classical examples of stratified spaces, such as…
The aim of these notes is to introduce the intuition motivating the notion of a "complicial set", a simplicial set with certain marked "thin" simplices that witness a composition relation between the simplices on their boundary. By varying…
We prove that Jardine's model category of simplicial presheaves can be obtained by localizing the `discrete' version at the collection of all hypercovers. One consequence is that the fibrant objects can be explicitly identified in terms of…
While many different models for $(\infty,1)$-categories are currently being used, it is known that they are Quillen equivalent to one another. Several higher-order analogues of them are being developed as models for $(\infty,…
By a result of Vallette, we put a sensible model structure on the category of conilpotent Lie coalgebras. This gives us a powerful tool to study the subcategory of Lie algebras obtained by linear dualization, also known as the category of…
This is a sequel to [1106.3772], in which a systematic study of cellular stratified spaces and related concepts was initiated. In this paper, we study important operations on cellular and stellar stratified spaces, including taking…
We record a particularly simple construction on top of Lumsdaine's local universes that allows for a Coquand-style universe of propositions with propositional extensionality to be interpreted in a category with subobject classifiers.
After explaining the importance of model categories in abstract homotopy theory, we provide concrete examples demonstrating that various categories of manifolds do not have all finite colimits, and hence cannot be model categories. We then…
Much of the homotopical and homological structure of the categories of chain complexes and topological spaces can be deduced from the existence and properties of the 'simple' functors Tot : {double chain complexes} -> {chain complexes} and…