Related papers: Adams' cobar construction revisited

Classical homological algebra takes place in additive categories. In homotopy theory such additive categories arise as homotopy categories of ``additive groupoid enriched categories'', in which a secondary analog of homological algebra can…

We study weak commutative algebras in a symmetric monoidal model category $\mathscr{M}$. We provide a model structure on these algebras for any symmetric monoidal model category that is combinatorial and left proper. Our motivation was to…

We consider families of reductive complexes related by level-raising operators and originating from an associative algebra. In the main theorem it is shown that the multiple cohomology of that complexes is given by the factor space of…

Given a span of spaces, one can form the homotopy pushout and then take the homotopy pullback of the resulting cospan. We give a concrete description of this pullback as the colimit of a sequence of approximations, using what we call the…

We introduce a type of surgery decomposition of Weinstein manifolds we call simplicial decompositions. The main result of this paper is that the Chekanov-Eliashberg dg-algebra of the attaching spheres of a Weinstein manifold satisfies a…

Let $\mathbf{X}$ be an Adams geometric stack. We show that $D(A_{qc}(\mathbf{X}))$, its derived category of quasi-coherent sheaves, satisfies the axioms of a stable homotopy category defined by Hovey, Palmieri and Strickland. Moreover we…

Simplicial versions of topological abelian gauge theories are constructed which reproduce the continuum expressions for the partition function and Wilson expectation value of linked loops, expressible in terms of R-torsion and linking…

We extend the bar-cobar adjunction to operads and properads, not necessarily augmented. Due to the default of augmentation, the objects of the dual category are endowed with a curvature. We handle the lack of augmentation by extending the…

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…

A recent pre-print of W\"arn gives a novel pen-and-paper construction of a type family characterizing the path spaces of an arbitrary pushout, and a natural language argument for its correctness. We present the first formalization of the…

Consider a diagram of quasi-categories that admit and functors that preserve limits or colimits of a fixed shape. We show that any weighted limit whose weight is a projective cofibrant simplicial functor is again a quasi-category admitting…

If $\mathbf{C}$ is a category with pullbacks then there is a bicategory with the same objects as $\mathbf{C}$, spans as morphisms, and maps of spans as 2-morphisms, as shown by Benabou. Fong has developed a theory of "decorated" cospans,…

J. S. Wilson proved in 1971 an isomorphism between the structural lattice associated to a group belonging to his second class of groups with every proper quotient finite and the Boolean algebra of clopen subsets of Cantor's ternary set. In…

In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse…

The Fedosov deformation quantization on a cotangent bundle with a symplectic connection induced by some linear symmetric connection on the base space is considered. A global construction of the symplectic homogeneous connection on the…

We show that for quasi-compact quasi-separated schemes of finite dimension, the constructibility condition in real \'etale cohomology agrees with a notion of constructibility arising naturally from topology. As application we prove that the…

This is the second of two papers in which we prove that a cell model of the moduli space of curves with marked points and tangent vectors at the marked points acts on the Hochschild co--chains of a Frobenius algebra. We also prove that a…

We prove that the shifted Hochschild chain complex $C\_*(A,A)[m]$ of a symmetric open Frobenius algebra $A$ of degree $m$ has a natural homotopy coBV-algebra structure. As a consequence $HH\_*(A,A)[m]$ and $HH^*(A,A^\vee)[-m]$ are…

In this paper we study the question of how to transfer homotopic structure from the category sD of simplicial objects in a fixed category D to D. To this end we use a sort of homotopy colimit s : sD --> D, which we call simple functor. For…

The $K$-theory of the stable Higson corona of a coarse space carries a canonical ring structure. This ring is the domain of an unreduced version of the coarse co-assembly map of Emerson and Meyer. We show that the target also carries a ring…