Goodwillie calculus and algebras over a spectral operad
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2013.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2013
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| Online Access: | http://hdl.handle.net/1721.1/82440 |
| _version_ | 1826209559179427840 |
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| author | Pereira, Luis Alexandre Meira Fernandes Alves |
| author2 | Mark J. Behrens. |
| author_facet | Mark J. Behrens. Pereira, Luis Alexandre Meira Fernandes Alves |
| author_sort | Pereira, Luis Alexandre Meira Fernandes Alves |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2013. |
| first_indexed | 2024-09-23T14:24:28Z |
| format | Thesis |
| id | mit-1721.1/82440 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T14:24:28Z |
| publishDate | 2013 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/824402019-04-10T09:03:13Z Goodwillie calculus and algebras over a spectral operad Pereira, Luis Alexandre Meira Fernandes Alves Mark J. Behrens. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics. Mathematics. 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. 2013-11-18T19:23:34Z 2013-11-18T19:23:34Z 2013 Thesis http://hdl.handle.net/1721.1/82440 862976302 eng 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 133 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Pereira, Luis Alexandre Meira Fernandes Alves Goodwillie calculus and algebras over a spectral operad |
| title | Goodwillie calculus and algebras over a spectral operad |
| title_full | Goodwillie calculus and algebras over a spectral operad |
| title_fullStr | Goodwillie calculus and algebras over a spectral operad |
| title_full_unstemmed | Goodwillie calculus and algebras over a spectral operad |
| title_short | Goodwillie calculus and algebras over a spectral operad |
| title_sort | goodwillie calculus and algebras over a spectral operad |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/82440 |
| work_keys_str_mv | AT pereiraluisalexandremeirafernandesalves goodwilliecalculusandalgebrasoveraspectraloperad |