Title: Cofibrations in Homotopy Theory
Author: Andrei Radulescu-Banu
Author's e-mail address: andrei@alum.mit.edu
Author's mailing address: 86 Cedar St, Lexington, MA 02421
Abstract: 

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