7 problems

String-diagram conjecture for dependence categories. The string diagrams for dependence categories should be similar to those presented for physical duoidal categories, with the on…

The discussion concerns reverse derivatives represented as lenses and optics in traced symmetric monoidal categories, with feedback supplied by the trace. Bidirectional information…

An $n$-signature is a set of generating morphisms in each dimension $k\leq n$, and an $n$-diagram is an $n$-dimensional string diagram formed by composing these generators. An $n$-…

Least-fixed-point conjecture. These copying and deleting operations force the star to be a single definite value: the least fixed point, rather than an arbitrary fixed point.

K-d tree equivalence conjecture. Equivalences of k-d trees should be the same as equivalences of proof trees. More broadly, brick diagrams whose underlying tiling is binarily compo…

Let $SD$ be the space of string diagrams, and let $sim$ be the equivalence relation on $SD$ described in the paper. Denote the harmonic compactification of the moduli space of Riem…

Let $SD$ be the space of string diagrams introduced by Drummond-Cole, Poirier, and Rounds, generalizing the spaces of chord diagrams. Let the moduli space of Riemann surfaces be de…