Polynomial Functors: A Mathematical Theory of Interaction [pdf]
I get that Category Theory is literally a highly theory-based branch of Mathematics, but would it kill its adherents to list an <i>actual</i> practical example?<p>I watched the associated talk[1], and David mentions that Poly is &quot;applicable to database migrations&quot;.<p>Okay, <i>how exactly</i>? What practical problems can I solve with it? Can anyone demonstrate Poly being used somehow for a 1000-table database migration more elegantly than could be achieved using other methods? Is there an O(n^2) or O(exp(n)) scaling lurking in there somewhere, or is this the magic sauce we&#x27;ve all been looking for?<p>Looking in from the outside, I get the distinct impression that category theorists tend to turn up, simply name things that other people have spent their lives working on, call it &quot;understood&quot;, and walk away as-if they&#x27;ve just explained everything that needs to be known about the topic they&#x27;ve merely labelled. They seem like the bug-collectors of mathematics. Okay fine, you&#x27;ve got an impressive collection of bugs, but have you understood evolution well enough from that to help industry with increasing pesticide resistance? Yes? No?<p>[1] <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=Cp5_o2lDqj0">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=Cp5_o2lDqj0</a>