There is no "Category of Categories"

The small categories and the functors between them do NOT form a large category. Though, there is a way to refine the arrows to get a "category of small categories" that isn't evil, but it's not as nice as you might first think. __________ Errata: 03:08 - The max degrees of these spaces of polynomials is one too high... oops. Thanks ‪@SvenBeh‬ (and also‪@Nicola_Bardini‬... and probably others ) __________ Timestamps: 00:00 - Introduction 00:53 - The category of categories 02:30 - Linear algebra, to a category theorist 03:43 - Equivalences of categories 04:49 - Fibre products of categories 07:37 - Fibre products of categories, done correctly 08:20 - The actual category of categories 11:10 - Evil fibre product 13:32 - Derived fibre product 15:13 - Homotopy fibre product 21:27 - Thx4watching