"A system is here defined as a set of objects together with relationships between the objects and between their attributes related to each other and to their environment so as to form a whole."is almost the same as that of a category in mathematical category
The difference is that in category theory the objects have no internal attributes or structure and that if an environment is necessary, it is represented as one or more additional objects.
If anyone has a tame professor of mathematics handy, I am sure there are several dissertations in this observation. (I cannot help much; I am still waiting for "Category Theory for the Slobbering Moron". But give me a footnote if you can.)