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arXiv:math/0610009 [math.AT]AbstractReferencesReviewsResources

Cofibrations in Homotopy Theory

Andrei Radulescu-Banu

Published 2006-09-30, updated 2009-02-08Version 4

We define Anderson-Brown-Cisinski (ABC) cofibration categories, and construct homotopy colimits of diagrams of objects in ABC cofibration categories. Homotopy colimits for Quillen model categories are obtained as a particular case. We attach to each ABC cofibration category a left Heller derivator. A dual theory is developed for homotopy limits in ABC fibration categories and for right Heller derivators. These constructions provide a natural framework for 'doing homotopy theory' in ABC (co)fibration categories.

Comments: Ams-latex, 158 pages. Corrections to Thm. 6.4.1 and Def. 7.2.5
Categories: math.AT, math.KT
Subjects: 18G55, 55U35, 18G10, 18G30, 55U10
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