He uses the work published in a previous article in SEMIOTICA , the Journal of the International Association for Semiotic Studies. It is entitled « The trichotomic machine »», vol. 2019, no. 228, May 2019, pp. 173-192 (ISSN 1613-3692, DOI: https://doi.org/10.1515/sem-2018-0084, 30 € ) and highlights the main points.
Here are the links and summaries:
The trichotomic machine brings order among the interpretants
Discussions on the number of trichotomies chosen by Charles S. Peirce to create and classify signs generated many diverse and varied opinions. This article implements the « trichotomic machine ». This machine is obtained by a mathematical modeling which uses only three basic definitions of algebraic theory of categories (category, functor, natural transformation of functors). It is carefully designed to ensure that it fits perfectly with Peirce’s statements on the issue. A computer application created by Patrick Benazet automates its operation when it is applied to suites of objects of thinking (phanerons in Peirce terminology) connected by successive determinations. The results are indisputable. These are well-known order structures called lattice. For cases of triadic and hexadic signs the results were validated a long time ago. However for decadic signs it is shown that the question is still open and that it would be imprudent to take for granted the 66 classes of signs.
The formal analysis of the principles leading the classification of the hexadic, decadic and triadic signs from C.S Peirce especially, gives rise to a general methodology allowing to systematically classify any n-adic combinatory named “protosign”. Basic concepts of the algebraic theory regarding the categories and functors will be used. That formalization provides an additional benefit by highlighting and systematizing formal immanent relationships between the classes of protosigns (or signs)[1]. Well known hierarchical structures (lattices) are then obtained. Thanks to the contribution of specific concepts in the Homological Algebra, new methodologies of analysis and creation of significations can be introduced.
[1] This relationships are called « affinities » by C. S. Peirce in CP 2.263 (case of the triadic signs).