Indexed on: 01 Sep '70Published on: 01 Sep '70Published in: Manuscripta Mathematica
The aim of this paper is to study some formal properties of fibrations (=continuous maps which have the covering homotopy property), cofibrations (=maps which have the homotopy extension property), h-fibrations (,6.4) and h-cofibrations(,2.2). We introduce the notion of a generalized homotopy system in a category (2). This notion will be selfdual. To show that fibrations and cofibrations, h-fibrations and h-cofibrations are dual notions, no use will be made of adjoint functors. Our approach admits the transition from a categoryC to other categories, e.g. to the categoryCB of objects over a given object B ofC.