Uhm. Well, I'd say his "later" albums, maybe starting with ISAM, are a lot more ambient and cinematic. I find these a bit more difficult to accomodate, compared to, say, Bricolage, which I adored. But now that you said it, I'm not sure I'm sufficiently familiar with his late later albums […]

Functors Lens → Set are the same thing as strong profunctors Setᵒᵖ x Set → Set (the Tambara representation theorem), so "dependent strong profunctors" on Set can probably be usefully *defined* to be functors Poly → Set

Anyways, let's look at a more delightful area for confusion. Remember Einstein summation? (pq)^i_k = p^i_j · q^j_k = sum_j p^i_j · q^j_k This summation looks a lot like our coend notation! In fact, that is exactly the kind of thing you would model using coends. It also explains why we might […]

Please, no more poetry, what's a coend?! It's what we need to do to combine two sets of arrows p(c,d) and q(d,e). (q o p)(c,e) = S^d p(c,d)×q(d,e) The composition q after p (q o p) should give a profunctor that returns all possible ways to get from c to e. Then the set of combined arrows has […]

A coend is a gadget to glue two profunctors together. A profunctor is a gadget to glue categories together. A category is a gadget to glue pairs of objects together. So... there's a cherry tree C above, and some dark blueberry shrubs D at our feet. A spider named P (friends call him Pavuk) has […]

A ring built from the Julia sets found along the main cardioid of the Mandelbrot set. one of my favourite mathematical objects

I spent so much time with just this thing the past few years. @matthen.com