What happens in a world without equality?   All you have are things, processes that turn one thing into another, meta-processes that turn one process to another, and so on... forever!   

If this is too scary you can truncate it at the nth level.  Then you're dealing with an 'n-category'.  This has things (called 'objects'), processes (called 'morphisms'), meta-processes (called '2-morphisms') and so on up to n-morphisms.

In this talk I explain the periodic table of n-categories - a fundamental structure that organizes our understanding of these . 

I put a lot of work into making it fun and easy to follow... and I think it worked!   

(Alas, the video quality is still not great, but it's better than last week's lecture where I introduced n-categories.   The volume is low so you have to really crank up your speaker... and the only way I have to boost the volume of a video also makes the file a lot bigger.)

https://www.youtube.com/watch?v=X1PkkqDwf8Y