اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPositive model structures for abstract symmetric spectra
128
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We give a general method of constructing positive stable model structures for symmetric spectra over an abstract simplicial symmetric monoidal model category. The method is based on systematic localization, in Hirschhorns sense, of a ceratin positive projective model structure on spectra, where positivity basically means the truncation of the zero slice. The localization above is by the set of stabilizing morphisms, or their truncated version.
قيم البحث
اقرأ أيضاً
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
egory construction for a bipermutative category. As an example, we use this machinery to construct a delooping of the K-theory of a bimonoidal category as defined by Baas-Dundas-Rognes.
We show that a derivator is stable if and only if homotopy finite limits and homotopy finite colimits commute, if and only if homotopy finite limit functors have right adjoints, and if and only if homotopy finite colimit functors have left adjoints.
These characterizations generalize to an abstract notion of stability relative to a class of functors, which includes in particular pointedness, semiadditivity, and ordinary stability. To prove them, we develop the theory of derivators enriched over monoidal left derivators and weighted homotopy limits and colimits therein.
We present a family of model structures on the category of multicomplexes. There is a cofibrantly generated model structure in which the weak equivalences are the morphisms inducing an isomorphism at a fixed stage of an associated spectral sequence.
Corresponding model structures are given for truncate
We initiate the study of model structures on (categories induced by) lattice posets, a subject we dub homotopical combinatorics. In the case of a finite total order $[n]$, we enumerate all model structures, exhibiting a rich combinatorial structure e
ncoded by Shapiros Catalan triangle. This is an application of previous work of the authors on the theory of $N_infty$-operads for cyclic groups of prime power order, along with new structural insights concerning extending choices of certain model structures on subcategories of $[n]$.
In this paper, we provide a new proof of the stable Adams conjecture. Our proof constructs a canonical null-homotopy of the stable J-homomorphism composed with a virtual Adams operation, by applying the $mathrm{K}$-theory functor to a multi-natural t
ransformation. We also point out that the original proof of the stable Adams conjecture is incorrect and present a correction. This correction is crucial to our main application. We settle the question on the height of higher associative structures on the mod $p^k$ Moore spectrum $mathrm{M}_p(k)$ at odd primes. More precisely, for any odd prime $p$, we show that $mathrm{M}_p(k)$ admits a Thomified $mathbb{A}_n$-structure if and only if $n < p^k$. We also prove a weaker result for $p=2$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
