Jesus - yes, this sum of powers algorithm is one thing I wish I'd had time to explain. Luckily it's nicely explained in _[Seven Sketches](http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf)_.
> Would it be correct to say that a resuorce theory sprung from a weighted graph as in the top post would have the limitation of single-ingredient, single-product boxes that the meringue pie chart doesn't verify?
Yes, that's another thing I didn't have time to get into. To understand multiple-input, multiple-output processes where each process has a cost (or time) we should use PERT charts or - more or less equivalently I think - timed Petri nets. I believe these give rise not to mere \\(\mathcal{V}\\)-categories but "symmetric monoidal \\(\mathcal{V}\\)-categories". However, I don't know of anybody who has developed the theory here yet in a systematic way. I think I could do it pretty quickly, but since I'm only allowing myself 3 weeks on each chapter I decided this would eat up too much of our limited time!
But that's one good thing about this course: it's giving me idea for more research projects.
> Would it be correct to say that a resuorce theory sprung from a weighted graph as in the top post would have the limitation of single-ingredient, single-product boxes that the meringue pie chart doesn't verify?
Yes, that's another thing I didn't have time to get into. To understand multiple-input, multiple-output processes where each process has a cost (or time) we should use PERT charts or - more or less equivalently I think - timed Petri nets. I believe these give rise not to mere \\(\mathcal{V}\\)-categories but "symmetric monoidal \\(\mathcal{V}\\)-categories". However, I don't know of anybody who has developed the theory here yet in a systematic way. I think I could do it pretty quickly, but since I'm only allowing myself 3 weeks on each chapter I decided this would eat up too much of our limited time!
But that's one good thing about this course: it's giving me idea for more research projects.
Version 2.1.8p2
