Related papers: Inductive LS cocategory and localisation

This paper constructs model structures on the categories of coalgebras and pointed irreducible coalgebras over an operad. The underlying chain-complex is assumed to be unbounded and the results for bounded coalgebras over an operad are…

Among cocomplete categories, the locally presentable ones can be defined as those with a strong generator consisting of presentable objects. Assuming Vop{\v{e}}nka's Principle, we prove that a cocomplete category is locally presentable iff…

Let X be a quasi-compact scheme, equipped with an open covering by affine schemes. A quasi-coherent sheaf on X gives rise, by taking sections over the covering sets, to a diagram of modules over the various coordinate rings. The resulting…

We generalize a recent result of Clausen: For a number field with integers O, we compute the K-theory of locally compact O-modules. For the rational integers this recovers Clausen's result as a special case. Our method of proof is quite…

Let V be a cofibrantly generated closed symmetric monoidal model category and M a model V-category. We say that a weighted colimit W*D of a diagram D weighted by W is a homotopy weighted colimit if the diagram D is pointwise cofibrant and…

We study the topology of X given that Cp(X) injects into Cp(Y), where Y is compact. We first show that if Cp over a GO-space (="subspace of a lineraly ordered space") injects into Cp over a compactum, then the Dedekind remainder of the…

Using the theory of resolving classes, we show that if $X$ is a CW complex of finite type such that $\map_*(X, S^{2n+1})\sim *$ for all sufficiently large $n$, then $\map_*(X, K) \sim *$ for every simply-connected finite-dimensional CW…

We prove that the cyclic chain complex of the categorical coalgebra of singular chains on an arbitrary topological space $X$ is naturally quasi-isomorphic to the $S^1$-equivariant chains of the free loop space of $X$. This statement does…

Let f: A\to B be a ring homomorphism between Noetherian normal integral domains. We establish a general criterion for f to induce a homomorphism Cl(f): Cl(A)\to Cl(B) on divisor class groups. For instance, this criterion applies whenever f…

We propose an inductive procedure to classify N-partite entanglement under stochastic local operations and classical communication (SLOCC) provided such a classification is known for N-1 qubits. The method is based upon the analysis of the…

We give a new criterion guaranteeing existence of model structures left-induced along a functor admitting both adjoints. This works under the hypothesis that the functor induces idempotent adjunctions at the homotopy category level. As an…

Let X be a C-infinity manifold. We construct a microlocalization functor $\mu_X$ from the derived category of bounded complexes of ind-sheaves on X to the one on the cotangent bundle of X. This functor generalizes the classical theory of…

Given $X$ a finite nilpotent simplicial set, consider the classifying fibrations $$ X\to Baut_G^*(X)\to Baut_G(X),\qquad X\to Z\to Baut_{\pi}^*(X), $$ where $G$ and $\pi$ denote, respectively, subgroups of the free and pointed homotopy…

If C=C_\phi denotes the mapping cone of an essential phantom map \phi from the suspension of the Eilenberg-Mac Lane complex K=K(Z,5) to the 4-sphere S=S^4 we derive the following properties: (1) The LS category of the product of C with any…

In this paper, we introduce a new class of structured spaces which is locally modeled by Costello's L-infinity spaces. This provides an alternative approach to study the derived geometric structures in the algebraic, analytic, or smooth…

For a subring $R$ of the rational numbers, we study $R$-localization functors in the local homotopy theory of simplicial presheaves on a small site and then in ${\mathbb A}^1$-homotopy theory. To this end, we introduce and analyze two…

The noncommutative stable homotopy category $\mathtt{NSH}$ is a triangulated category that is the universal receptacle for triangulated homology theories on separable $C^*$-algebras. We show that the triangulated category $\mathtt{NSH}$ is…

We say that a group G has cohomology almost everywhere finitary if and only if the nth cohomology functors of G commute with filtered colimits for all sufficiently large n. In this paper, we show that if G is a group in Kropholler's class…

The purpose of this paper is to explain why the functor that sends a stratified topological space $S$ to the $\infty$-category of constructible (hyper)sheaves on $S$ with coefficients in a large class of presentable $\infty$categories is…

We show that in the category of groups, every singly-generated class which is closed under isomorphisms, direct limits and extensions is also singly-generated under isomorphisms and direct limits, and in particular is co-reflective. We also…