Yoneda Lemma Visualized
Boring comments: Representables are of course defined up to isomorphism. To complete the last part into a proof of the Yoneda lemma, one needs to perform a straightforward check of all sorts of compatibilities. When I sloppily write \alpha e, I actually mean the component of \alpha on the set over which e hangs. The “integral” presheaf in the presheaf party is constant. Made with: for animation: Manim for editing: CapCut for sounds: Caustic for narration: NaturalReader Any suggestions for another video are welcome Timestamps: 0:00 - Intro 0:43 - Presheaf introduction 1:17 - Presheaf maps 2:09 - The representable 3:42 - The universal property of a free object 4:46 - The representable as a free object 5:46 - Outro
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