The following questions should be very easy, but I need help. Notations are same as Bredon's geometry and topology book. This question is related to chapter VII.3.page 441. $\nabla \colon X\vee X\rightarrow X$ denotes the codiagonal, $S$ denotes the reduced suspension operation.
Q1:Is every example of H-cogroups given by the pair $(\nabla, S)?$ In other words, is it possible to obtain a H-cogroup which is not given by suspensions? Could you give me some references where they discuss these objects,play with $\nabla$ and change the fibers of the Serre fibrations accordingly?
Q2: Does it make sense to ask if the inclusion $J_f\subset S^n$ is a cofibration where $f\colon S^n\rightarrow S^n$ and $J_f$ is the Julia set of $f?$ (I should admit that I haven't spent time on this question yet, please skip it if it is too general)