| It sounds like you would be interested in the book / course '7 Sketches in Compositionality' by David Spivak and Brendan Fong, which studies precisely those ideas categorically, with a particular focus on systems that you might broadly call 'computational': http://math.mit.edu/~dspivak/teaching/sp18/ It has been discussed on Hacker News at least a couple of times previously -- fairly recently, even. You might be interested to look at these discussions: https://news.ycombinator.com/item?id=20376325 https://news.ycombinator.com/item?id=19701767 Edit to add: You might also be interested to learn that categorical approaches to linguistics typically take as their starting point monoidal categories, in which there are notions of 'parallel' as well as 'sequential' composition. It turns out that the usual categorical semantics for linguistics shares a lot with the categorical semantics for quantum mechanics: roughly, meanings are vectors, like quantum states. You can read more about doing (finite-dimensional) quantum mechanics entirely using string diagrams (the formal diagrammatic calculus of monoidal categories) in the work of Bob Coecke, who also played a large part in originating these approaches to linguistics. For example, on the quantum side, an excellent book is 'Picturing Quantum Processes' [0]. And on the linguistics side, the paper linked in the article is a good start: https://arxiv.org/abs/1003.4394 [0] Not freely available, but some slides are at https://www.cs.ox.ac.uk/ss2014/programme/Bob.pdf Edit, again: There is also of course Bartosz Milewski's book / blog series 'Category Theory for Programmers', which introduces category theory from the perspective of Haskell and C++ programming: https://bartoszmilewski.com/2014/10/28/category-theory-for-p... But the best introduction to category theory I have read is Leinster's book, 'Basic Category Theory': https://arxiv.org/abs/1612.09375 And as you might have guessed, I do agree with your statement! |
so?