David Spivak has done lots of cool work on applying category theory to many concrete systems like databases [1]. Brendan Fong has worked on applying category t

David Spivak has done lots of cool work on applying category theory to many concrete systems like databases [1]. Brendan Fong has worked on applying category theory to things that act like interconnected networks, such as electrical circuits. This fits into a larger ambitious program that John Baez is part of to use category theory to understand physical systems that are still much too complicated to understand with current mathematical tools, such as ecosystems. Fong's thesis is on my reading list [2]. The two authors are doing great research, like this investigation of the algebra of backpropagation [3]. I really look forward to reading this too! [1] https://arxiv.org/abs/0904.2012 https://arxiv.org/abs/0904.2012 [2] https://arxiv.org/abs/1609.05382 https://arxiv.org/abs/1609.05382 [3] https://arxiv.org/abs/1711.10455 https://arxiv.org/abs/1711.10455