Related papers: Completions of pro-spaces

The category of simplicial R-coalgebras over a presheaf of commutative unital rings on a small Grothendieck site is endowed with a left proper, simplicial, cofibrantly generated model category structure where the weak equivalences are the…

An n-truncated model structure on simplicial (pre-)sheaves is described having as weak equivalences maps that induce isomorphisms on certain homotopy sheaves only up to degree n. Starting from one of Jardine's intermediate model structures…

For finite coverings we elucidate the interaction between transferred Chern classes and Chern classes of transferred bundles. This involves computing the ring structure for the complex oriented cohomology of various homotopy orbit spaces.…

Let $T$ be the theory of dense cyclically ordered sets with at least two elements. We determine the classifying space of $\mathsf{Mod}(T)$ to be homotopically equivalent to $\mathbb{CP}^\infty$. In particular,…

The homotopy theory of representations of nets of algebras over a (small) category with values in a closed symmetric monoidal model category is developed. We illustrate how each morphism of nets of algebras determines a change-of-net…

Wright showed that, if a 1-ended simply connected locally compact ANR Y with pro-monomorphic fundamental group at infinity admits a proper Z-action, then that fundamental group at infinity can be represented by an inverse sequence of…

Since Quillen proved his famous equivalences of homotopy categories in 1969, much work has been done towards classifying the rational homotopy types of simply connected topological places. The majority of this work has focused on rational…

Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the…

This is a survey paper on cohomology theories for $A_\infty$ and $E_\infty$ ring spectra. Different constructions and main properties of topological Andr\'e-Quillen cohomology and of topological derivations are described. We give sample…

Lada introduced strong homotopy algebras to describe the structures on a deformation retract of an algebra in topological spaces. However, there is no satisfactory general definition of a morphism of strong homotopy (s.h.) algebras. Given a…

We define closed model category structures on different categories connected to the world of operad algebras over the category C(k) of (unbounded) complexes of k-modules: on the category of operads, on the category of algebras over a fixed…

Simplicial presheaves on cartesian spaces provide a general notion of smooth spaces. There is a corresponding smooth version of the singular complex functor, which maps smooth spaces to simplicial sets. We consider the localisation of the…

We construct a Quillen model structure on the category of spectral categories, where the weak equivalences are the symmetric spectra analogue of the notion of equivalence of categories.

For a commutative noetherian ring A, we compare the support of a complex of A-modules with the support of its cohomology. This leads to a classification of all full subcategories of A-modules which are thick (that is, closed under taking…

We construct a 2-equivalence $\mathfrak{CohTheory}^\text{op} \simeq \mathfrak{TypeSpaceFunc}$. Here $\mathfrak{CohTheory}$ is the 2-category of positive theories and $\mathfrak{TypeSpaceFunc}$ is the 2-category of type space functors. We…

Cohomology of a topological space with coefficients in stacks of abelian 2-groups is considered. A 2-categorical analog of the theorem of Grothendieck is proved, relating cohomology of the space with coefficients in a 2-stage spectrum and…

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

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 construct a new model structure on the category of dg presheaves over a topological space $X$, obtained through the right Bousfield localization of the local projective model structure. The motivation for this construction arises from…

Over a monoidal model category, under some mild assumptions, we equip the categories of colored PROPs and their algebras with projective model category structures. A Boardman-Vogt style homotopy invariance result about algebras over…