Related papers: Simplicial Descent Categories

We define a cobordism category of topological manifolds and prove that if $d \neq 4$ its classifying space is weakly equivalent to $\Omega^{\infty -1} MTTop(d)$, where $MTTop(d)$ is the Thom spectrum of the inverse of the canonical bundle…

Faltings' approach in $p$-adic Hodge theory can be schematically divided into two main steps: firstly, a local reduction of the computation of the $p$-adic \'etale cohomology of a smooth variety over a $p$-adic local field to a Galois…

Modular functors, i.e. consistent systems of projective representations of mapping class groups of surfaces, have been constructed for non-semisimple modular categories already decades ago. Concepts from homological algebra have not been…

Every smooth manifold contains particles which propagate. These form objects and morphisms of a category equipped with a functor to the category of Abelian groups, turning this into a 0+1 topological field theory. We investigate the…

The theory of abelian categories proved very useful, providing an axiomatic framework for homology and cohomology of modules over a ring and, in particular, of abelian groups. For many years, a similar categorical framework has been lacking…

The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. In this paper, the second in a series on "higher props," we show that the category of all small colored…

We give a construction of triangulated categories as quotients of exact categories where the subclass of objects sent to zero is defined by a triple of functors. This includes the cases of homotopy and stable module categories. These…

There is a construction which lies at the heart of descent theory. The combinatorial aspects of this paper concern the description of the construction in all dimensions. The description is achieved precisely for strict n-categories and…

We use Cisinski's machinery to construct and study model structures on the category of simplicial sets whose classes of fibrant objects generalize quasi-categories. We identify a lifting condition which captures the homotopical behavior of…

Making the first steps towards a classification of simple partial comodules, we give a general construction for partial comodules of a Hopf algebra \(H\) using central idempotents in right coideal subalgebras and show that any…

In this master thesis, we extend results from classical simple homotopy theory to the world of stratified homotopy theory. To obtain a well-established framework to work in, we prove a series of results on two model categories of simplicial…

We identify the obstructions for the functoriality and the uniqueness of the totalization functor, (partially) defined on the category of simplicial objects in the homotopy category of a stable model category, and we use a result from the…

We are concerned with the center (=quantum double) of tensor categories and prove generalizations of several results proven previously for quantum doubles of Hopf algebras. We consider F-linear tensor categories C with simple unit and…

The most natural notion of a simplicial nerve for a (weak) bicategory was given by Duskin, who showed that a simplicial set is isomorphic to the nerve of a $(2,1)$-category (i.e. a bicategory with invertible $2$-morphisms) if and only if it…

We establish an explicit comparison between two constructions in homotopy theory: the left adjoint of the homotopy coherent nerve functor, also known as the rigidification functor, and the Kan loop groupoid functor. This is achieved by…

The natural problem we approach in the present paper is to show how the notion of formally smooth (co)algebra inside monoidal categories can substitute that of (co)separable (co)algebra in the study of splitting bialgebra homomorphisms.…

We compare Friedlander's definition of the etale topological type for simplicial schemes to another definition involving realizations of pro-simplicial sets. This can be expressed as a notion of hypercover descent for etale homotopy. We use…

We introduce new methods for understanding the topology of $\Hom$ complexes (spaces of homomorphisms between two graphs), mostly in the context of group actions on graphs and posets. We view $\Hom(T,-)$ and $\Hom(-,G)$ as functors from…

It is proved that the category of simplicial complete bornological spaces over $\mathbb R$ carries a combinatorial monoidal model structure satisfying the monoid axiom. For any commutative monoid in this category the category of modules is…

We construct a derived generalization of the pure spinor superfield formalism and prove that it exhibits an equivalence of dg-categories between multiplets for a supertranslation algebra and equivariant modules over its Chevalley-Eilenberg…