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Peiyuan Zhu (Dec 31 2021 at 22:10):Is topos offering an alternative way of formulating dynamical system than differential equations? I looked at this document which seems to say something like this but I couldn't understand it very well. http://www.acsu.buffalo.edu/~wlawvere/ToposMotion.pdf
John Baez (Dec 31 2021 at 22:23):Topos theory gives a different way of thinking about differential equations, but not really an "alternative" to differential equations. As usual, we don't "throw things out" - we just do them better. I wrote about Lawvere's work on topos theory, synthetic differential geometry and dynamical systems here.
John Baez (Dec 31 2021 at 22:35):However, I should add that very little work has been done on dynamical systems using topos theory, and if I wanted to study dynamical systems more (which I occasionally do), topos theory would not be near the top of my list for things to learn about.