Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2013. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 131-133). / 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]. / by Luis Alexandre Meira Fernandes Alves Pereira. / Ph.D.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/82440 |
| Date | January 2013 |
| Creators | Pereira, Luis Alexandre Meira Fernandes Alves |
| Contributors | Mark J. Behrens., Massachusetts Institute of Technology. Department of Mathematics., Massachusetts Institute of Technology. Department of Mathematics. |
| Publisher | Massachusetts Institute of Technology |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 133 pages, application/pdf |
| 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., http://dspace.mit.edu/handle/1721.1/7582 |
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