Introduction to Category Theory 1: Course Overview

Brief history of category theory, followed by a discussion of what it is and how it is meant to be used. Discussed syllabus and format.

Now that I've figured out SketchBookExpress and Camtasia, future lectures will hopefully be less choppy and more punctual.

P.S. I forgot to mention in the video that my history of category theory is mostly fabricated. For a real/better timeline, see http://en.wikipedia.org/wiki/Timeline...

This is a University of Reddit course. The course page may be found at http://ureddit.com/class/36451/, and the official discussion site at http://www.reddit.com/r/URIntroCatego....

• Category

  Education

[eigenlambda]

video (17:50) says that the tensor product of two modules over the reals are the coproduct, wikipedia says the coproduct is the direct sum

[error792]

17:50 says that the tensor product of two *algebras* is the coproduct

[XetXetable]

Since I brought up the subject of unprofessionalism, I think I should highlight the history part of the video. You yourself acknowledge that the history was bogus, but you kept that part in anyway. You can use YouTube to edit out the clip so people don't waste their time, or better yet, redo that section with a more accurate history.

[error792]

I'm not trying to teach math history. The history section was just there to see the evolution of category theory in different directions (algebraic, logical, geometric, etc.), so I cherry-picked certain highlights; whether it's truthful isn't the point. The "mostly fabricated" comment is just my sense of humour, despite being made up off the top of my head it's pretty close to the truth.

[XetXetable]

You also stated that set theory is "wrapped up in annoying formalism", implying that category theory is not. This is false, considering category theory is ENTIRELY formalism (just like a lot of other subjects). Also, the formalism in set theory isn't annoying to most. Your own personal problems with working in a field you aren't even teaching shouldn't carry over to a lecture, it's just unprofessional and colors a student’s opinion in a way that will disbenefit them.

[error792]

I think the formalism of set theory is no longer very relevant to most mathematicians. I've never explicitly gone through the rigorous construction of addition or cardinal numbers (though I have a good idea of how to do so), and like most mathematicians I'll never need to.

[error792]

As for unprofessionalism... this isn't a formal university course; even if it were, it's pretty common for profs to say that set theory and general topology are dead, or to make fun of other fields of mathematics. I just chill out and ramble about math while having fun with colors. Have you seen the later videos? lol

[SonOfNye]

Please do not let this become a project that never gets finished. Thank you.

[aneeley]

You basically just cursed him.

[XetXetable]

What?

[mphello]

12m6s You perfectly described my exaggerated hopes that if I could just finally understand category theory, all of life's mathematical (and non-math) problems will be solved instantly. Well, to be fair to myself, when I read all the glowing hype about the importance and power of the great works of Grothendieck, et al etc, since I'm not skilled enough to judge it, I feel I have to go along with it.

[mphello]

Siiigh.

[filter80808]

Very informative and at times hilarious video.  Thanks so much!

[navidsonpuzzle]

Great video that very much appeals to my way of understanding things and communicating - thanks, error792! I think it's quite surprising, and unfortunate for others, that you're new to teaching.

[LadislauFernandes]

You stop posting!!! That is a crime against mathematics! Please post...

[Evi1M4chine]

Don’t listen to those Haskell tutorials, that say monads are hard, and/or use stupid analogies (all of them!). They are just really shitty at explaining it themselves, because they block their own mind with thinking it *must* be that hard, for everyone to parrot that around. And they cause you to fall into that same irrational mindset.

Only look at Haskell’s class definition for monads. Seriously! You will understand it much faster without those confusing tutorials!

[Pavlo Ferrum]

muchas gracias

[madjestic]

Loved the video!