idc, such that for all objects X pi,:X - IX -* X is the identity of X for r = 0 and e = 1. 1). (12) Push out axiom: For a cofibration i:B-+A and a map f there exists the push out 3 Categories with a natural cylinder 19 A ------ ),AUX lB X B f where 1 is also a cofibration. Moreover, the functor I carries the push out diagram into a push out diagram, that is I(AUBX)=IAUIBIX. Moreover, 10 = 0. (I3) Cofibration axiom: Each isomorphism is a cofibration and for each object X the map 0 -> X is a cofibration.
Here X u IA is the push out ofX<-