Philosophical Sketches on Category Theory Applied to Music-Mathematical Polar Semiotics

This is an attempt to combine Matthai philosophy (of Heraclitan inspiration) and Category Theory using the Yoneda Lemma as a means for harmonizing the traditionally opposite values and conceptions dissociated between the Euclidean tradition and Heraclitus thought. The text is divided in three sections: general background and description of Yoneda, a contextualization on Heraclitan aesthetics and polar semiotics (a notion firstly intuited by I. M. Lotman and Th. Sebeok), and an experiment suggested for the revision of the grounds of music theory, with the purpose of conciliate extremely dissociated notions of music (Euclidean vs. Heraclitan) however making part of a common musical experience and knowledge. Conclusions are addressed to hypothesize that Yoneda lemma may support a robust philosophy of music within the field of Category Theory where any group is isomorphic to a subgroup of a permutation, with one-to-one paired correspondences.