Goodwillie calculus and algebras over a spectral operad

The overall goal of this thesis is to apply the theory of Goodwillie calculus to the category Algo of algebras over a spectral operad. Its first part generalizes many of the original results of Goodwillie in [14] so that they apply to a larger class of model categories and hence be applicable to Algo. The second part then applies that generalized theory to the Algo categories. The main results here are: an understanding of finitary homogeneous between such categories; identifying the Taylor tower of the identity in those categories; showing that finitary n-excisive functors can not distinguish between Algo and Algo,, the category of algebras over the truncated operad O<; and a weak form of the chain rule between the algebra categories, analogous to the one found in [1].

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2013

Author dc:creator

• Pereira, Luis Alexandre Meira Fernandes Alves

Advisor dc:contributor.advisor

• Mark J. Behrens.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/82440

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/82440