Related papers: Homotopical resolutions associated to deformable a…

This is a (slightly edited) version of the PhD dissertation of the author, submitted to Brown University in July 2005. We construct a homotopy calculus of functors in the sense of Goodwillie for the categories of rational homotopy theory.…

Let $\mathbb{k}$ be a commutative ring with global dimension zero. We show that we can rigidify homotopy coherent comodules in connective modules over the Eilenberg-Mac Lane spectrum of $\mathbb{k}$. That is, the $\infty$-category of…

Dendroidal sets have been introduced as a combinatorial model for homotopy coherent operads. We introduce the notion of fully Kan dendroidal sets and show that there is a model structure on the category of dendroidal sets with fibrant…

The Andr\'e-Quillen cohomology of an algebra with coefficients in a module is defined by deriving a functor based on K\"ahler differential forms. It can be computed using a cofibrant resolution of the algebra in a model category structure…

We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral…

We prove that the classical result asserting that the relative Picard group of a faithfully flat extension of commutative rings is isomorphic to the first Amitsur cohomology group stills valid in the realm of symmetric monoidal categories.…

We consider the terminal monad among those preserving the objects of a subcategory, and in particular preserving the image of a monad. Several common monads are shown to be uniquely characterized by the property of being terminal objects in…

We investigate several categories related to transition structures, using a mixture of algebraic and topological methods. We show how two such categories are connected by a contravariant adjunction. This is the most detailed of a family of…

The aim of this paper is to construct exact model structures from so called extendable cotorsion pairs. Given a hereditary Hovey triple $(\mathcal{C}, \mathcal{W}, \mathcal{F})$ in a weakly idempotent complete exact category with enough…

For a 1-connected spectrum E, we study the moduli space of suspension spectra which come equipped with a weak equivalence to E. We construct a spectral sequence converging to the homotopy of the moduli space in positive degrees. In the…

We introduce regular sequences and associated Koszul resolutions for monoids in the category of functors over an essentially small linear symmetric monoidal category. Next we define polynomials over such monoids. We compute the Hochschild…

We prove that the bounded derived category of coherent sheaves with proper support is equivalent to the category of locally-finite, cohomological functors on the perfect derived category of a quasi-projective scheme over a field. We…

We introduce the notions of mixed resolutions and simplicial sections, and prove a theorem relating them. This result is used (in another paper) to study deformation quantization in algebraic geometry.

We work out the details of a correspondence observed by Goodwillie between cosimplicial spaces and good functors from a category of open subsets of the interval to the category of compactly generated weak Hausdorff spaces. Using this, we…

Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as…

Goodwillie's calculus of homotopy functors associates a tower of polynomial approximations, the Taylor tower, to a functor of topological spaces over a fixed space. We define a new tower, the varying center tower, for functors of categories…

The Godement cosimplicial resolution is available for a wide range of categories of sheaves. In this paper we investigate under which conditions of the Grothendieck site and the category of coefficients it can be used to obtain fibrant…

We establish new results on weighted $L^2$ extension of holomorphic top forms with values in a holomorphic line bundle, from a smooth hypersurface cut out by a holomorphic function. The weights we use are determined by certain functions…

In this paper, we consider compatible Hom-associative algebras as a twisted version of compatible associative algebras. Compatible Hom-associative algebras are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie…

Exact categories are a natural generalisation of abelian categories and provide a fertile ground to develop relative homological algebra. In this paper, starting from a class of relative Gorenstein projective objects in an exact category…