Enriched homotopy and calculus

منو

" Enriched homotopy and calculus "
Peter J. Oman T. Goodwillie

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 calculus\ Peter 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