Categories 7 Yoneda's lemma

This lecture is part of an online course on categories.
Any object of a category can be thought of as a representable functor in the category of presheaves.
We give several examples of representable functors. Then we state Yoneda's lemma, which roughly that morphisms of objects are he same as morphisms of the corresponding presheaves.
For the other lectures in the course see • Categories for the idl...

[@peterg2836]

Eons ago, a grad school friend of mine, a category theorist (or model theorist, perhaps?), pointed out/joked that Yoneda's lemma is 'even' more the absolute tautology than it at first might seem... Namely, the statement of Yoneda's lemma is that an object is determined by the morphisms to the object, while its proof is that, in particular, it is determined by the identity. [Very nice lecture - of course!]

[@samueldeandrade8535]

Hahaha. That's exactly right ...

[@lellosbarello90]

It's always a pleasure professor, thanks for your time and wish you a lovely weekend

[@andrewgibson7797]

Please don't stop this course! Very much want to learn category theory from you. These are excellent.

[@SquidGuy11]

I may be from a different university, but this explanation of Yoneda's lemma helped me understand it better. Thank you for that.

[@strangeWaters]

6:00 is very cool. I didn't know cohomology and homotopy were linked in that way.

[@vert4836]

I am taking a first year graduate course in algebra and these videos helped a lot! Thank you professor.

[@OffTheGridBand1]

I would like to just say thank you for your amazing channel. I am in the process of getting onto a funded Ph.D program and need something to keep myself on top of everything.

[@OffTheGridBand1]

Also its going to be at Aston in Birmingham :)

[@big-lion]

@@OffTheGridBand1 congratulatiosn

[@yt-1161]

who knows what a Scheme over Spec k is or what are line bundles ? Examples make it look more complicated, I’ve seen this in many other videos too. But once you learnt the basics your lectures really help to better understand.

[@andreas9333]

friday saved, prof

[@fakhryasad6348]

Thank You Professor for the best lecture.

[@TheRevAlokSingh]

I remember full as surjective because the source fills/covers the target

[@migarsormrapophis2755]

yeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

[@s.l.2227]

22:57 Faithful means injective. I can never remember the name for surjective. 😂