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Document Type:Latin Dissertation
Language of Document:English
Record Number:53546
Doc. No:TL23500
Call number:‭3272028‬
Main Entry:Peter J. Oman
Title & Author:Enriched homotopy and calculusPeter J. Oman
College:Brown University
Date:2007
Degree:Ph.D.
student score:2007
Page No:78
Abstract:In this work we develop a categorical foundation for homotopy calculus based on simplicial enrichment. In particular, the homotopical category of homotopy functors will be replaced by a model structure on an appropriate diagram category. Categorical enrichment over symmetric monoidal categories, in general, is reviewed and using change-of-base 2-functors the special case of enrichment over symmetric spectra is exploited. Standard Yoneda arguments classify operators and give models for the Maclaurin tower of a finitary homotopy functor from simplicial sets to spectra. We conclude with remarks regarding a generalization to local operators applicable to the Taylor tower.
Subject:Pure sciences; Enriched homotopy; Homotopy calculus; Mathematics; 0405:Mathematics
Added Entry:T. Goodwillie
Added Entry:Brown University