In “Natural duality, Modality, and Coalgebras”, in his thesis Meaning and Duality - From Categorical Logic to Quantum Physics, and elsewhere Yoshihiro Maruyama talks about $\mathrm{ISP}$, $\mathrm{ISP}$(M), how it is composed of $\mathrm{I}$, $\mathrm{S}$ and $\mathrm{P}$, but I can’t figure out what these stand for.

]]>"Deep insights about groups are not obtained by studying universal algebra. Nor

will universal coalgebra lead to di cult theorems about (speci c types of) systems.

Like universal algebra, its possible merit consists of the fact that it tidies up

a mass of rather trivial detail, allowing us to concentrate our powers on the hard

core of the problem"

After reading some articles I should start to believe this quote, but the question is - is there possible to consider some more concrete (more refined) structures than coalgerbas and arrive at less general (more practical) results. Judging from the algebra courses, on can expect (at least by playing with words) that cogroups (and their representations) could be really fruitful objects of research. But there are so little literature about them. Why is so? I can guess - maybe all the results for cogroups can be trivially achived from the group theory? Maybe mathematicians don't see the perspective in this field and so on?

From reading ncatlab topics I can understand that the term "cogroup" is used in two meanings - as cogroup object and simply as cogroup. I am more interested in the later - cogroup as special case of coalgebra. ]]>