Lecture one of six in an introductory set of lectures on category theory.
Take Away from the lecture: Morphisms are just as important as the objects that they morph. Many different types of mathematical constructions are best described using morphisms instead of elements. (This isn’t how things are typically taught however.)
Would have been nice to have some more discussion of the required background for those new to the broader concept. There were a tremendous number of examples from many areas of higher math that many viewers wouldn’t have previously had. I think it’s important for them to know that if they don’t understand a particular example, they can move on without much loss as long as they can attempt to apply the ideas to an area of math they are familiar with. Having at least a background in linear algebra and/or group theory are a reasonable start here.
In some of the intro examples it would have been nice to have seen at least one more fully fleshed out to better demonstrate the point before heading on to the multiple others which encourage the viewer to prove some of the others on their own.
Thanks for these Steven, I hope you keep making more! There’s such a dearth of good advanced math lectures on the web, I hope these encourage others to make some of their own as well.