Related papers: A monoidal Dold-Kan correspondence for comodules

This paper can be thought of as an extended introduction to arXiv:0708.3398; nevertheless, most of its results are not covered by loc. cit. We consider the derived categories of DG-modules, DG-comodules, and DG-contramodules, the coderived…

Let $k$ be an algebraically closed field and $A$ a $\mathbb{Z}$-graded finitely generated simple $k$-algebra which is a domain of Gelfand-Kirillov dimension 2. We show that the category of $\mathbb{Z}$-graded right $A$-modules is equivalent…

In this article, we extend Sullivan's PL de Rham theory to obtain simple algebraic models for the rational homotopy theory of parametrised spectra. This simplifies and complements the results of arXiv:1910.14608, which are based on…

We prove an analogue of the Gabriel--Quillen embedding theorem for exact $\infty$-categories, giving rise to a presentable version of Klemenc's stable envelope of an exact $\infty$-category. Moreover, we construct a symmetric monoidal…

This is the author's diploma thesis. We describe a simplification in the construction of Khovanov-Rozansky's categorification of quantum sl(n) link homology using the theory of maximal Cohen-Macaulay modules over hypersurface singularities…

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…

Using Quillen-Lurie deformation theory formalism we develop an obstruction theory for studying the stable $\infty$-category of modules over a given geometric $\infty$-stack. The obstruction theory studies the problem of lifting compact…

Diagrammatic sets admit a notion of internal equivalence in the sense of coinductive weak invertibility, with similar properties to its analogue in strict $\omega$-categories. We construct a model structure whose fibrant objects are…

We study the covariant model structure on dendroidal spaces and establish direct relations to the homotopy theory of algebras over a simplicial operad as well as to the homotopy theory of special $\Gamma$-spaces. As an important tool in the…

Using ideas from shape theory we embed the coarse category of metric spaces into the category of direct sequences of simplicial complexes with bonding maps being simplicial. Two direct sequences of simplicial complexes are equivalent if one…

We extend the Quillen Theorem Bn for homotopy fibers of Dwyer, et al. to similar results for homotopy pullbacks and note that these results imply similar results for zigzags in the categories of relative categories and k-relative…

Our aim is to give a fairly complete account on the construction of compatible model structures on exact categories and symmetric monoidal exact categories, in some cases generalizing previously known results. We describe the close…

This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through *-autonomous monoidal categories and related structures.

We discover a new connection between Koszul theory and representation theory. Let $\La$ be a quadratic algebra defined by a locally finite quiver with relations. Firstly, we give a combinatorial description of the local Koszul complexes and…

Given a left Quillen presheaf of localized model structures, we study the homotopy limit model structure on the associated category of sections. We focus specifically on towers and fibered products (pullbacks) of model categories. As…

We construct a pseudo-localization of the 2-category of combinatorial Quillen model categories with respect to Quillen equivalences, and then verify that it embeds in a 2-category of Grothendieck derivators.

In this paper we show that the Matsushita model structure on loop graphs, which is right-transferred from the Kan-Quillen model structure on simplicial sets, factors through two other right-transferred model structures on simplicial…

In this paper we study quasi-categories of comodules over coalgebras in a stable homotopy theory. We show that the quasi-category of comodules over the coalgebra associated to a Landweber exact S-algebra depends only on the height of the…

Given a good homology theory E and a topological space X, the E-homology of X is not just an E_{*}-module but also a comodule over the Hopf algebroid (E_{*}, E_{*}E). We establish a framework for studying the homological algebra of…

The paper establishes an equivalence between directed homotopy categories of (diagrams of) cubical sets and (diagrams of) directed topological spaces. This equivalence both lifts and extends an equivalence between classical homotopy…