Thanks for your thoughts and for the link! I definitely agree that we are very far from practical category-inspired improvements at this stage; I simply wonder whether there isn’t something fundamentally as simple and novel as differential equations waiting around the corner and that we are taking a very circuitous route toward through very deep metamathematics! (Baez’s rosetta stone paper and work by Abramsky and Coeck on quantum logic have convinced me that we need something like “not being in a Cartesian category” to account for notions like context and meaning, but that quantum stuff is only one step removed from the most Cartesian classical logic/physics and we probably need to go to the other extreme to find a different kind of simplicity)
Thanks for your thoughts and for the link! I definitely agree that we are very far from practical category-inspired improvements at this stage; I simply wonder whether there isn’t something fundamentally as simple and novel as differential equations waiting around the corner and that we are taking a very circuitous route toward through very deep metamathematics! (Baez’s rosetta stone paper and work by Abramsky and Coeck on quantum logic have convinced me that we need something like “not being in a Cartesian category” to account for notions like context and meaning, but that quantum stuff is only one step removed from the most Cartesian classical logic/physics and we probably need to go to the other extreme to find a different kind of simplicity)
No problem!
Do you mean monoidal categories? I think that’s what the central concept in the Abramsly-Coeke work & the Baez Rosetta stone paper is.