So you are in favor of integral notation for coends? Why not a sum-sigma instead? Product-pi made it, but as you say, there's simply no pendant for calculus. Maybe it became an integral-s because sigma appears in logic, as symbol set and elsewhere.
Context, where I give up on writing the perfect coend explainer, because I have more questions:
https://mathstodon.xyz/@RefurioAnachro/117237458422243698
Bartosz Milewski (npub1glg…tqzy)