Related papers: Spectral enrichments of model categories

We give a new proof that for a finite group G, the category of rational G-equivariant spectra is Quillen equivalent to the product of the model categories of chain complexes of modules over the rational group ring of the Weyl group of H in…

We prove that continuous spectrum- and commutativity-preserving maps to $\mathcal{M}_n(\mathbb{C})$ from the space of normal (real or complex) $n\times n$, $n\ge 3$ matrices with spectra contained in a given continuous-injection interval…

The $2$-primary Hopf invariant $1$ elements in the stable homotopy groups of spheres form the most accessible family of elements. In this paper we explore some properties of the $\mathcal{E}_\infty$ ring spectra obtained from certain…

We study the homotopy right Kan extension of homotopy sheaves on a category to its free cocompletion, i.e. to its category of presheaves. Any pretopology on the original category induces a canonical pretopology of generalised coverings on…

We construct combinatorial model category structures on the categories of (marked) categories and (marked) pre-additive categories, and we characterize (marked) additive categories as fibrant objects in a Bousfield localization of…

In this paper we use the formalism of S.Weinberg in order to construct a mathematical model based on the weak decay of hadrons and nuclei. In particular we consider a model which generalizes the weak decay of the nucleus of the cobalt. We…

The Ziegler spectrum for categories enriched in closed symmetric monoidal Grothendieck categories is defined and studied in this paper. It recovers the classical Ziegler spectrum of a ring. As an application, the Ziegler spectrum as well as…

We show that weak monoidal Quillen equivalences induce equivalences of symmetric monoidal $\infty$-categories with respect to the Dwyer-Kan localization of the symmetric monoidal model categories. The result will induce a Dold-Kan…

We construct a symmetric spectrum representing the G-equivariant K-theory of C*-algebras for a compact group or a proper groupoid G. Our spectrum is functorial for equivariant *-homomorphisms. We use this to establish the additivity of the…

For an arbitrary symmetric monoidal $\infty$-category $\mathcal{V}$, we define the factorization homology of $\mathcal{V}$-enriched $(\infty,1)$-categories over (possibly stratified) 1-manifolds and study some of its basic properties. In…

We show that any closed model category of simplicial algebras over an algebraic theory is Quillen equivalent to a proper closed model category. By ``simplicial algebra'' we mean any category of algebras over a simplicial algebraic theory,…

We introduce here a natural functional associated to any $b \in QH_* (M, \omega)$: \emph{spectral length functional}, on the space of "generalized paths" in $ \text {Ham}(M, \omega)$, closely related to both the Hofer length functional and…

We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…

For the category $\mathscr V$ of complex algebraic varieties, the Grothendieck group of the commutative monoid of the isomorphism classes of correspondences $X \xleftarrow f M \xrightarrow g Y$ with proper morphism $f$ and smooth morphism…

Let M be a monoidal category endowed with a distinguished class of weak equivalences and with appropriately compatible classifying bundles for monoids and comonoids. We define and study homotopy-invariant notions of normality for maps of…

We extend some classical results of Bousfield on homology localizations and nilpotent completions to a presentably symmetric monoidal stable $\infty$-category $\mathscr{M}$ admitting a multiplicative left-complete $t$-structure. If $E$ is a…

We apply the Dwyer-Kan theory of homotopy function complexes in model categories to the study of mapping spaces in quasi-categories. Using this, together with our work on rigidification from [DS1], we give a streamlined proof of the Quillen…

Over the complex numbers, the complement of a collection of hyperplanes is a widely-studied object; the cohomology ring, in particular, is known to have a structure depending only on the combinatorial properties of the intersection of…

Every homology or cohomology theory on a category of E-infinity ring spectra is Topological Andre-Quillen homology or cohomology with appropriate coefficients. Analogous results hold for the category of A-infinity ring spectra and for…

We prove that various structures on model $\infty$-categories descend to corresponding structures on their localizations: (i) Quillen adjunctions; (ii) two-variable Quillen adjunctions; (iii) monoidal and symmetric monoidal model…