ترغب بنشر مسار تعليمي؟ اضغط هنا

Iterated traces in 2-categories and Lefschetz theorems

87   0   0.0 ( 0 )
 نشر من قبل Kate Ponto
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

While not obvious from its initial motivation in linear algebra, there are many context where iterated traces can be defined. In this paper we prove a very general theorem about iterated 2-categorical traces. We show that many Lefschetz-type theorems in the literature are consequences of this result and the new perspective we provide allows for immediate spectral generalizations.



قيم البحث

اقرأ أيضاً

205 - Nick Gurski , Niles Johnson , 2015
We establish an equivalence of homotopy theories between symmetric monoidal bicategories and connective spectra. For this, we develop the theory of $Gamma$-objects in 2-categories. In the course of the proof we establish strictfication results of ind ependent interest for symmetric monoidal bicategories and for diagrams of 2-categories.
Picard 2-categories are symmetric monoidal 2-categories with invertible 0-, 1-, and 2-cells. The classifying space of a Picard 2-category $mathcal{D}$ is an infinite loop space, the zeroth space of the $K$-theory spectrum $Kmathcal{D}$. This spectrum has stable homotopy groups concentrated in levels 0, 1, and 2. In this paper, we describe part of the Postnikov data of $Kmathcal{D}$ in terms of categorical structure. We use this to show that there is no strict skeletal Picard 2-category whose $K$-theory realizes the 2-truncation of the sphere spectrum. As part of the proof, we construct a categorical suspension, producing a Picard 2-category $Sigma C$ from a Picard 1-category $C$, and show that it commutes with $K$-theory in that $KSigma C$ is stably equivalent to $Sigma K C$.
211 - Rune Haugseng 2014
We construct higher categories of iterated spans, possibly equipped with extra structure in the form of local systems, and classify their fully dualizable objects. By the Cobordism Hypothesis, these give rise to framed topological quantum field theories, which are the fram
We prove the equivalence of several hypotheses that have appeared recently in the literature for studying left Bousfield localization and algebras over a monad. We find conditions so that there is a model structure for local algebras, so that localiz ation preserves algebras, and so that localization lifts to the level of algebras. We include examples coming from the theory of colored operads, and applications to spaces, spectra, and chain complexes.
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 e circle, the tensor with $X$ is topological Hochschild homology over $R$. We use the theory of localizations of $infty$-categories as a technical tool: we contribute to this theory an $infty$-categorical analogue of Days reflection theorem about closed symmetric monoidal structures on localizations, and we prove that for a smashing localization $L$ of the $infty$-category of presentable $infty$-categories, the free $L$-local presentable $infty$-category on a small simplicial set $K$ is given by presheaves on $K$ valued on the $L$-localization of the $infty$-category of spaces. If $X$ is a pointed space, a map $g: Ato B$ of $E_infty$-ring spectra satisfies $X$-base change if $Xotimes B$ is the pushout of $Ato Xotimes A$ along $g$. Building on a result of Mathew, we prove that if $g$ is etale then it satisfies $X$-base change provided $X$ is connected. We also prove that $g$ satisfies $X$-base change provided the multiplication map of $B$ is an equivalence. Finally, we prove that, under some hypotheses, the Thom isomorphism of Mahowald cannot be an instance of $S^0$-base change.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا