摘要 :
This is a continuation, completion, and generalization of our previous joint work [3] with Boris Chorny. We supply model structures and Quillen equivalences underlying Goodwillie's constructions on the homotopy level for functors ...
展开
This is a continuation, completion, and generalization of our previous joint work [3] with Boris Chorny. We supply model structures and Quillen equivalences underlying Goodwillie's constructions on the homotopy level for functors between simplicial model categories satisfying mild hypotheses.
收起
摘要 :
The homotopy theory of small functors is a useful tool for studying various questions in homotopy theory. In this paper, we develop the homotopy theory of small functors from spectra to spectra, and study its interplay with Spanie...
展开
The homotopy theory of small functors is a useful tool for studying various questions in homotopy theory. In this paper, we develop the homotopy theory of small functors from spectra to spectra, and study its interplay with Spanier–Whitehead duality and enriched representability in the dual category of spectra. We note that the Spanier–Whitehead duality functor D: Sp→Sp~(op) factors through the category of small functors from spectra to spectra, and construct a new model structure on the category of small functors, which is Quillen equivalent to Sp~(op) . In this new framework for the Spanier–Whitehead duality, Sp and Sp~(op) are full subcategories of the category of small functors and dualization becomes just a fibrant replacement in our new model structure.
收起
摘要 :
We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define homotopy n–nilpotent groups as homotopy algebras over certain simplicial algebraic...
展开
We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define homotopy n–nilpotent groups as homotopy algebras over certain simplicial algebraic theories. This notion interpolates between infinite loop spaces and loop spaces, but backwards. We study the relation to ordinary nilpotent groups. We prove that n–excisive functors of the form ΩF factor over the category of homotopy n –nilpotent groups.
收起
摘要 :
The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure [B. Chorny, W.G. Dwyer, Homotopy theory of small diagrams over large categories, preprint, 2005]. In this pap...
展开
The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure [B. Chorny, W.G. Dwyer, Homotopy theory of small diagrams over large categories, preprint, 2005]. In this paper we construct various localizations of the projective model structure and also give a variant for functors from simplicial sets to spectra. We apply these model categories in the study of calculus of functors, namely for a classification of polynomial and homogeneous functors. In the n-homogeneous model structure, the nth derivative is a Quillen functor to the category of spectra with Σn-action. After taking into account only finitary functors—which may be done in two different ways—the above Quillen map becomes a Quillen equivalence. This improves the classification of finitary homogeneous functors by T.G. Goodwillie [T.G. Goodwillie, Calculus. III. Taylor series, Geom. Topol. 7 (2003) 645–711 (electronic)].
收起
摘要 :
We achieve a classification of $n$-types of simplicial presheaves in terms of $(n-1)$-types of presheaves of simplicial groupoids. This can be viewed as a description of the homotopy theory of higher stacks. As a special case we o...
展开
We achieve a classification of $n$-types of simplicial presheaves in terms of $(n-1)$-types of presheaves of simplicial groupoids. This can be viewed as a description of the homotopy theory of higher stacks. As a special case we obtain a good homotopy theory of (weak) higher groupoids.
收起
原文获取