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). 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.
Peirce, Charles S. 1931–1966. The collected papers of Charles S. Peirce, vol. 8. C. Hartshorne, P. Weiss & A. W. Burks (eds.). Cambridge: Harvard University Press. [Reference to Peirce’s papers will be designated CP followed by volume and paragraph number.].
Peirce, Charles S. 1976. The new elements of mathematics, vol. 4. C. Eisele (ed.). Berlin & New York: Mouton de Gruyter. Atlantic Highlands, NJ: Humanities Press. [Reference to Peirce’s New Elements will be designated NEM followed by volume and page number].
Peirce, Charles S. & Lady Victoria Welby. 1977. Semiotic and significs. Charles S. Hardwick (ed.). Bloomington: Indianapolis University Press. [Reference to this work will be designated SS followed by page number].