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Yoneda Lemma Slides, Interpreting Yoneda Lemma, Yoneda Lemma

International Category Theory Conference

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Sample papers

• Applied Category Theory 2022

Yoneda Lemma as Knowledge Switch. An Outsider's View of Category Theory as Metaphor Theory.

I lead Math 4 Wisdom, an investigatory community for absolute truth. I relate a language of wisdom (in terms of cognitive frameworks) with the language of mathematics (at a graduate student level). Wisdom - the knowledge of everything - is the content. Math - the study of structure - is the form.

I have documented a language of cognitive frameworks which I dare call a language of wisdom. But how could I validate it? I could say that whenever we divide everything into four perspectives, our minds are dealing with the issue of knowledge, and we have four levels of knowledge: whether, what, how, why. I could argue that every thinker, in their private language, refers to these four levels - Aristotle, Plato, Peirce. But how can we go beyond our private languages and develop a shared language? I am exploring how to do that by appealing to examples in mathematical thinking.

For example, consider a short exact sequence and/or related chain complex which consists of four maps.

Or consider, in recursion theory, the Arithmetic Hierarchy.

But I will appeal to the Yoneda lemma. And the reason is the Yoneda perspective. So let me illustrate the four levels of knowledge with a cup.

And compare them with four ways of thinking about the Yoneda lemma.

Yoneda lemma -

Anthropologically speaking - mathematicians are the greatest problem in the world.

Beauty - based on the line between inside and outside.

Category theory plays on this line, moving us from colimits to limits.

Everything is that which has no external context and no internal structure. So it serves as a starting point.