اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Combinatorics of Iterated Loop Spaces
156
0
0.0
(
0
)
تأليف
M.A. Batanin
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
It is well known since Stasheffs work that 1-fold loop spaces can be described in terms of the existence of higher homotopies for associativity (coherence conditions) or equivalently as algebras of contractible non-symmetric operads. The combinatorics of these higher homotopies is well understood and is extremely useful. For $n ge 2$ the theory of symmetric operads encapsulated the corresponding higher homotopies, yet hid the combinatorics and it has remain a mystery for almost 40 years. However, the recent developments in many fields ranging from algebraic topology and algebraic geometry to mathematical physics and category theory show that this combinatorics in higher dimensions will be even more important than the one dimensional case. In this paper we are going to show that there exists a conceptual way to make these combinatorics explicit using the so called higher nonsymmetric $n$-operads.
قيم البحث
اقرأ أيضاً
This paper proves three different coherence theorems for symmetric monoidal bicategories. First, we show that in a free symmetric monoidal bicategory every diagram of 2-cells commutes. Second, we show that this implies that the free symmetric monoida
l bicategory on one object is equivalent, as a symmetric monoidal bicategory, to the discrete symmetric monoidal bicategory given by the disjoint union of the symmetric groups. Third, we show that every symmetric monoidal bicategory is equivalent to a strict one. We give two topological applications of these coherence results. First, we show that the classifying space of a symmetric monoidal bicategory can be equipped with an E_{infty} structure. Second, we show that the fundamental 2-groupoid of an E_n space, n geq 4, has a symmetric monoidal structure. These calculations also show that the fundamental 2-groupoid of an E_3 space has a sylleptic monoidal structure.
In this article we discuss a relation between the string topology and differential forms based on the theory of Chens iterated integrals and the cyclic bar complex.
Cartesian fibrations were originally defined by Lurie in the context of quasi-categories and are commonly used in $(infty,1)$-category theory to study presheaves valued in $(infty,1)$-categories. In this work we define and study fibrations modeling p
resheaves valued in simplicial spaces and their localizations. This includes defining a model structure for these fibrations and giving effective tools to recognize its fibrations and weak equivalences. This in particular gives us a new method to construct Cartesian fibrations via complete Segal spaces. In addition to that, it allows us to define and study fibrations modeling presheaves of Segal spaces.
We prove that four different ways of defining Cartesian fibrations and the Cartesian model structure are all Quillen equivalent: On marked simplicial sets, on bisimplicial spaces, on bisimplicial sets, on marked simplicial spaces. The main way to pro
ve these equivalences is by using the Quillen equivalences between quasi-categories and complete Segal spaces as defined by Joyal-Tierney and the straightening construction due to Lurie.
Mittag-Leffler condition ensures the exactness of the inverse limit of short exact sequences indexed on a partially ordered set $(I,leq)$ admitting a $countable$ cofinal subset. We extend Mittag-Leffler condition by relatively relaxing the countabili
ty assumption. As an application we prove an ultrametric analogous of a result of V.P.Palamodov in relation with the acyclicity of Frechet spaces with respect to the completion functor.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
