I love this guy's enthusiasm.

A great lecture! That said, if in the future there is a way to have the camera pointed directly at the board rather than at an angle it would be extremely helpful.

My friends and I have been doing a reading group of Vakil’s book—this was such a gem to find. Thank you!

Nothing like a full board of definitions to begin a topic.

I remember my calculus teacher at the time, talking about sheaf theory and cohomology and the math you need to get there. 6:04, 23:26

thank you very much for making this available to a larger audience! ❤️❤️

thank you

Great presenter

Less interrupting to display vast knowledge and superiority, more interrupting to ask genuine questions and propose clarifications.

Very nice job. I really enjoyed the whole lecture. It cleared up a few things for me.

Very pleasant video.

so helpful and i love it!

Beautiful example at the end of the lecture!

THANKS FOR SHEAVES

It was really help full for me,thank you ....Nickolas Rollick sir

so good thank you

Scheaves

nice explanation

The Lecturer is so patient! omg what's the target audience of this class......

Note that one can turn contravariant functors in to covariant with a simple change of wording: Any functor on the open sets with morphisms as inclusion/subset can be converted in to that of a functor who's morphisms are the superset relationship. This flips the direction of the arrows but more importantly shows that it's all about language. We tend to think in terms of subsets rather than super sets and so when we map that concept to other categories the directions may be inverted from what we think(sorta mirror image) because the natural direction, in this example, would be to use supersets rather than subsets.