11,543 research outputs found
Calculus of functors and model categories
The category of small covariant functors from simplicial sets to simplicial
sets supports the projective model structure. 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 -homogeneous model structure, the -th
derivative is a Quillen functor to the category of spectra with
-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.Comment: 22 pages. Exposition is substantially improved. Few minor mistakes
are correcte
Goodwillie's Calculus of Functors and Higher Topos Theory
We develop an approach to Goodwillie's calculus of functors using the
techniques of higher topos theory. Central to our method is the introduction of
the notion of fiberwise orthogonality, a strengthening of ordinary
orthogonality which allows us to give a number of useful characterizations of
the class of -excisive maps. We use these results to show that the pushout
product of a -equivalence with a -equivalence is a
-equivalence. Then, building on our previous work, we prove a
Blakers-Massey type theorem for the Goodwillie tower. We show how to use the
resulting techniques to rederive some foundational theorems in the subject,
such as delooping of homogeneous functors.Comment: 40 pages, (a slightly modified version of) this paper is accepted for
publication by the Journal of Topolog
- …