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What use is the Yoneda lemma? - Mathematics Stack Exchange Serre's observation is literally a consequence of the statement of the Yoneda lemma, but I think the "philosophy" of the Yoneda lemma is also very important; namely, one can characterize an object by how other objects map into it
Can someone explain the Yoneda Lemma to an applied mathematician? I have trouble following the category-theoretic statement and proof of the Yoneda Lemma Indeed, I followed a category theory course for 4-5 lectures (several years ago now) and felt like I underst
Basic Example of Yoneda Lemma? - Mathematics Stack Exchange The Yoneda lemma proves that the direct style of programming and the continuation-passing style of programming are equivalent (naturally isomorphic) Indeed, consider the datatypes returned by the direct and continuation-passing variants
What is the origin of the expression “Yoneda Lemma”? The Yoneda Lemma made an early appearance in the work of the Japanese pioneer N Yoneda (private communication to Mac Lane) [1954]; with time, its importance has grown
Yoneda product in the cohomology of a truncated polynomial algebra A reference relating this to the above Yoneda product is Gelfand-Manin - Methods of Homological Algebra, Theorem III 5 5 c Added later: For what it's worth, here's a high-tech reason why xy = − yx Let R = k[X, Y] be the free commutative algebra over k on symbols X and Y
What limits colimits are preserved by the Yoneda embedding? I know that the contravariant Yoneda embedding X ↦ C(−, X) X ↦ C (−, X) preserves all small limits that exist in C C I guess it follows that the covariant Yoneda embedding preserves all colimits But what happens if we have a case in which a limit (rather than a colimit) appears in the first argument of hom, i e we have a functor of the form C(lim←−Xi, −) C (lim ← X i, −
Stacky Yoneda lemma - Mathematics Stack Exchange I’m studying differentiable stacks from this paper (Gregory Ginot), and I’m trying to understand why the “Yoneda embedding” from the category of differentiable manifolds $\\textbf{Man}$ to the categ
How do you explicitly form the dual of the Yoneda lemma? Can you explicitly explain how you formed the dual of the Yoneda lemma? What did you do to each part of the Yoneda lemma that resulted in leaving everything the same except for the functor D(−, r) D (−, r)? And how is the bijective map defined in the dual?
Is the Yoneda completion of the rationals the extended real line? A thing that I have often heard is that, when viewed as an enriched category, the Yoneda embedding of the poset of rationals $\\mathbb{Q}$ into its category of presheaves is just the dense embedding