>>13117797>Yoneda's lemmain terms of universal algebra
http://boole.stanford.edu/pub/yon.pdffor application
https://ncatlab.org/nlab/show/Yoneda+lemma#applications7. Applications
The Yoneda lemma is the or a central ingredient in various reconstruction theorems, such as those of Tannaka duality. See there for a detailed account.
In its incarnations as Yoneda reduction the Yoneda lemma governs the algebra of ends and coends and hence that of bimodules and profunctors.
The Yoneda lemma is effectively the reason that Isbell conjugation exists. This is a fundamental duality that relates geometry and algebra in large part of mathematics.
For isbell dualities,
http://www.tac.mta.ca/tac/volumes/20/15/20-15.pdfbut gelfand duality is a classical result in maths, so learn this and then generalize it to isbell duality.
https://en.wikipedia.org/wiki/Gelfand_dualityIn mathematics, the Gelfand representation in functional analysis (named after I. M. Gelfand) has two related meanings:
a way of representing commutative Banach algebras as algebras of continuous functions;
the fact that for commutative C*-algebras, this representation is an isometric isomorphism.
In the former case, one may regard the Gelfand representation as a far-reaching generalization of the Fourier transform of an integrable function. In the latter case, the Gelfand–Naimark representation theorem is one avenue in the development of spectral theory for normal operators, and generalizes the notion of diagonalizing a normal matrix.
