John Carlos Baez on Nostr: - People are generally bad at explaining coends, for lots of reasons. As Bartosz ...

- People are generally bad at explaining coends, for lots of reasons. As Bartosz Milewski (npub1glg…tqzy) hinted, profunctors are an easy generalization of matrices, and coends then give a generalization of matrix multiplication. You multiply matrices by moving your left finger horizontally along a row while moving your right finger vertically along a column, taking products of matrix entrries and adding them up. Composing profunctors using a coend is just like that.

This makes the idea of coend easy to understand. People usually clutter up a first explanation with lots of other things, like ends, or dinatural transformations, or... whatever. It's better to wait on those.