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)


Thank you. 



Examples of H-cogroups and a question about julia sets
Regarding question (1), the answer is that there are co-groups which aren't suspensions.


Berstein, Israel; Harper, John R.
Cogroups which are not suspensions. Algebraic topology (Arcata, CA, 1986), 63–86, 
Lecture Notes in Math., 1370, Springer, Berlin, 1989. 


A cogroup is a co-H-space with an associative comultiplication and an inversion. The paper gives the first examples of spaces which are cogroups but are not homotopy equivalent to a suspension. These examples are 2- and 3-cell complexes. The proofs involve delicate piecing together of homotopies and detailed information about homotopy groups of spheres.


