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# Yoav R. Kallus

• 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…
• 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…