Category Theory - Three Translations of the Yoneda Lemma

Last modified by Ivak Iroovvud on 2020/01/02 12:17

http://titleduntitled.name/facades/3translations.pdf

To define the mathematical objects we intend to study, we often - perhaps always - first make it understood, more often implicitly than explicitly, how we intend these objects to be presented to us, thereby delineating a kind of super-object; that is, a species of mathematical objects garnished with a repertoire of modes of presentation. Only once this is done do we try to erase the scaffolding of the presentation, to say when two of these super-objects - possibly presented to us in wildly different ways - are to be considered equal. In this oblique way, the objects that we truly want enter the scene only defined as equivalence classes of explicitly presented objects. That is, as specifically presented objects with the specific presentation ignored, in the spirit of "ham and eggs, but hold the ham."
 (BARRY MAZUR, When is One Thing Equal to Some Other Thing?)

1920px-Yoneda_lemma_cd.svg.png

Language Game: Three Translations of the Yoneda Lemma

I present a "literary translation'' of the Yoneda Lemma, a statement in categorical algebra, into a piece of prose writing, followed by some commentary. This project hopes to investigate the cultural activity of mathematics as a linguistic and aesthetic practice, and to see what happens when some of the patterns in a piece of mathematical writing are used in the seemingly quite foreign context of literary writing. A brief discussion of the motivation, influences, execution, and questions behind it follows.

Theory: Category Theory

Category Theory is a 20th century field of math describing structural similarities between mathematical models, essentially by considering the functions that represent objects in those theories. There is some debate as to whether it is itself a theory, or something more like a notation system, a "language." Either way, category theory encodes some of some of the most abstract advances in mathematics in the past half-century, the kind no one other than mathematicians hear about.

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Created by Qfwfq on 2019/01/27 00:35
    

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Titled, "Untitled" - Kavi Duvvoori - The Committee Made in Charge of Such Matters - Please Reuse or Distribute Further Only With a Measure of Generosity, Care, and Sense