Goodwillie calculus and algebras over a spectral operad
Name
862976302-MIT.pdf
Description
Full printable version
Size
7.06 MB
Format
Adobe PDF
Checksum (MD5)
23ff15a60d62df56c9f16d332d8423e1
Author(s)
Pereira, Luis Alexandre Meira Fernandes Alves
Advisor(s)
Mark J. Behrens.
Date Issued
2013
Publisher
Massachusetts Institute of Technology
Abstract
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].
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2013.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 131-133).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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