Mutual Dependency Relationship and Category Theory

As it is Tribute to John Stewart our remarks refer to a working group which met regularly at the UTC and at the IHPST between 2014 and 2016 and which had as central concern the modeling of living organization and the development of certain mathematical formalisms favorable to this modeling. First, we briefly recall the heart of the work carried out by this informal working group. Then in a second step, we evoke in more detail the position of John Stewart relative to this problematic in particular his analysis of the work of Robert Rosen. Finally, in a third and final step, we propose to present some recent works resulting from a critical reading of an article by Mossio, Longo and Stewart (2009) dealing with the Rosen conjecture. We take up the resolution of Rosen's equations in lambda-calculus and propose an implementation in Haskell as well as a new interpretation of his causal graphs in terms of autocategories, a variant of the categories used by Andrée Ehresmann and Jean-Paul Vanbremeersch for the modeling and understanding of living and cognitive systems.