%0 Generic %1 radulescubanu2006cofibrations %A Radulescu-Banu, Andrei %D 2006 %K homotopy %T Cofibrations in Homotopy Theory %U http://arxiv.org/abs/math/0610009 %X 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.

@misc{radulescubanu2006cofibrations, abstract = {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.}, added-at = {2015-03-10T06:53:19.000+0100}, author = {Radulescu-Banu, Andrei}, biburl = {https://www.bibsonomy.org/bibtex/26fb42df8e845ce607068ae3ebcb40e8b/t.uemura}, description = {[math/0610009] Cofibrations in Homotopy Theory}, interhash = {d082076b166ce1a9b9d93c15a7d85cd8}, intrahash = {6fb42df8e845ce607068ae3ebcb40e8b}, keywords = {homotopy}, note = {cite \href{http://arxiv.org/abs/math/0610009}{arxiv:math/0610009}Comment: Ams-latex, 158 pages. Corrections to Thm. 6.4.1 and Def. 7.2.5}, timestamp = {2015-03-10T06:53:19.000+0100}, title = {Cofibrations in Homotopy Theory}, url = {http://arxiv.org/abs/math/0610009}, year = 2006 }