Forme e Comportamenti: temi categoriali nella teoria dei sistemi

In the present thesis we explore the rich interface between Category Theory and General Systems Theory. After reviewing the seminal work on systems carried out by Francisco J. Varela, Joseph A. Goguen and Louis H. Kauffman in the seventies, we try to give a modern categorical presentation of some of its aspects, exploiting subsequent developments of the language of categories. In particular, we rely upon the (dual) idioms of universal algebra and uni- versal coalgebra: we present an introduction to the relevant theory, showing how the main concepts are rooted in a description of the interaction between system and environment, intended as abstract entities. Finally, as an extended running example, we describe the (pictorial) mathematics of George Spencer- Brown’s Laws of Form, which was saluted by general systems theorists as a unifying language. We offer a presentation of its main features in modern terms, remarking the interesting conceptual challenges it raises, and then try to elucidate some of them, exploiting once again the previous semanti- cal tools.