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# Yoav R. Kallus

## Comments

• Scott, your snake equation proof looks good, except that you only show that the two profunctors are equal along the diagonal. That is, you only show that for all $$x$$, [ (1_X \times \cup_X ) (\cap_X \times 1_X )((1,x),(x,1)) = 1_X(x,x) ] You need t…
• But Puzzle 209 is about something more specific. So, let me give some hints. In Puzzle 209 the feasibility relation we're calling $$\Phi$$ is just any old feasibility relation from $$\mathbb{N}$$ to $$\mathbb{N}$$: it's a very famous on…
• John, so far information theory and statistics have been most applicable to my new work. I've been having fun following the course and have already had a few of the supernova concept collapse moments of the kind you mentioned in Lecture 17.
• James, I studied physics in grad school. I was always on the more theoretical side, but I didn't actually become a mathematician until after grad school, when I was a postdoc fellow.
• The dual lattice doesn't seem to be closed either. If we know "how to relate 1 to 2" and we want to know "how to relate 1, 2, and 3", we can either learn "how to relate 1 to 3" or "how to relate 2 to 3". But if you told me that all you know is eithe…
• I was doing some reading to catch up with the class and I learned about the Adjoint Functor Theorem in Lecture 16. So now I know how to prove that $$R_3 = \mathrm{Ob}:\mathbf{Poset}\to\mathbf{Set}$$ doesn't have a right adjoint. We need to show tha…
• Puzzle 194. From Lecture 11 we know that for any set $$X$$ the set of partitions of $$X$$, $$\mathcal{E}(X)$$, becomes a poset with $$P \le Q$$ meaning that $$P$$ is finer than $$Q$$. It's a monoidal poset with product given by the meet $$P \wedg… • Bat, yes, and because \(L_1$$ and $$L_2$$ drop objects when acting on non-discrete things, I was worried the composition wouldn't end up giving back Disc, which doesn't drop objects. But it turned out the resolution is that $$L_3$$ only spits out di…
• I had worked out a solution of the original version of Puzzle 163, even though it later turned out not to be intended as stated. Puzzle 163. Show there are functors [ \mathbf{Cat} \stackrel{R_1}{\longrightarrow} \mathbf{Preord} \stackrel{R_…