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
