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We define a right Cartan-Eilenberg structure on the category of Kans combinatorial spectra, and the category of sheaves of such spectra, assuming some conditions. In both structures, we use the geometric concept of homotopy equivalence as the strong equivalence. In the case of sheaves, we use local equivalence as the weak equivalence. This paper is the first step in a larger-scale program of investigating sheaves of spectra from a geometric viewpoint.
We prove that the set of concordance classes of sections of an infinity-sheaf on a manifold is representable, extending a theorem of Madsen and Weiss. This is reminiscent of an h-principle in which the role of isotopy is played by concordance. As an
Let $f:Gto mathrm{Pic}(R)$ be a map of $E_infty$-groups, where $mathrm{Pic}(R)$ denotes the Picard space of an $E_infty$-ring spectrum $R$. We determine the tensor $Xotimes_R Mf$ of the Thom $E_infty$-$R$-algebra $Mf$ with a space $X$; when $X$ is th
We show how to construct a Gamma-bicategory from a symmetric monoidal bicategory, and use that to show that the classifying space is an infinite loop space upon group completion. We also show a way to relate this construction to the classic Gamma-cat
We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories ${mathcal D}_{2n}$. The categories we use are that of coherent sheaves on Springer fibers over a nilpotent element of $sl_{2n}$
We consider categories of generalized perverse sheaves, with relaxed constructibility conditions, by means of the process of gluing $t$-structures and we exhibit explicit abelian categories defined in terms of standard sheaves categories which are eq