11:11 Generative effects. 14:19 Sets. 16:26 Product sets. 18:51 Set theory is not a convenient foundation for Mathematics. 19:50 Subsets. 20:57 Relations. 25:29 Functions. 28:46 One to one functions. 29:47 Notation for functions. 30:53 Surjections. 31:40 Partitions are surjections. 34:34 Order on partitions. 43:03 What is an order. 45:26 Order creates join. 46:59 Summary and the announcement of the future lectures.
I have been studying Category Theory on my own for about 6 months now as part of an Independent Study with University. I wish I would have found this course closer to the beginning of the semester, it's crazy to me how few courses on Category Theory there are when it's basically the foundation of pure mathematics. Thank you for this!
I know this is pretty late, but maybe somebody finds it useful. I think that the property that you missed is the 'commute' part, that is, the diagram of arrows must commute. We have p1: A ->> P1, and p2: A->>P2. Now, you say you can define a function f: P2 -> P1, which is true, but can it ever commute with the rest of diagram as such: ¿f;p2 = p1? . As p1 is surjective and f is not surjective with a little bit of hand waving, i think that f;p2 cannot ever be equal to p1.
Regarding Type Theory... There exists a topology of Human Types... It is a continuous topology... Which is why my Grandmother, a Jew, had to die. Because she was topologically close to QEII... She died of Lung Cancer, though she never smoked. RAND CORP stuff...
