What kinds of graphs? There are a number of graphical representations that turn out to be incredibly useful in category theory, but they're far from equivalent. IIRC, https://arxiv.org/abs/1803.05316 introduces some of them.
Just saying objects and morphisms. The types of each are found in CT, which abstract-up to these, but are bounded/encompassed by the limits we know of regarding elementary ideas like cliques, cycles, paths, colouring, various morphisms.
Compression, folding, encoding, and other information theory ideas have analogues represented as these, and the bottom up/depth first search of the problem space seems to come at it from the wrong direction.
We're well into indulging Internet crank territory here but I'm naively speculating that for every known theorem, there is a consistent object/morphism representation of it, and the rules we're getting good at finding for these relationships (graphs) will yield insights we were missing for lack of an encompassing consistent abstraction.
Comments
What kinds of graphs? There are a number of graphical representations that turn out to be incredibly useful in category theory, but they're far from equivalent. IIRC, https://arxiv.org/abs/1803.05316 introduces some of them.
Just saying objects and morphisms. The types of each are found in CT, which abstract-up to these, but are bounded/encompassed by the limits we know of regarding elementary ideas like cliques, cycles, paths, colouring, various morphisms.
Compression, folding, encoding, and other information theory ideas have analogues represented as these, and the bottom up/depth first search of the problem space seems to come at it from the wrong direction.
We're well into indulging Internet crank territory here but I'm naively speculating that for every known theorem, there is a consistent object/morphism representation of it, and the rules we're getting good at finding for these relationships (graphs) will yield insights we were missing for lack of an encompassing consistent abstraction.