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Asad Saeeduddin (Mar 28 2022 at 10:24):Sorry to ask such a vague and ridiculous question, but is there such a thing as an adjunction between the kinematics and dynamics of moving systems? Or alternately, would someone have pointers to some kind of categorical treatment of the connection between systems involving mappings of space and their rates of change and distributions of mass/energy/momenta and their rates of change?
Simon Burton (Mar 29 2022 at 11:24):I'm a big fan of vague and ridiculous questions. The first thing that occurs to me is to think of this in the quantum context. You can think of the position and momentum operators as acting on a graded commutative algebra, with position having grade +1, and momentum having grade -1. The Heisenberg commutation relations don't look like adjoint functors yet, but where's my shoehorn...
Peter Arndt (Apr 21 2022 at 19:01):I don't quite understand what you are after, but did you check out Lawvere's writings on laws of motion? See the references here (but not necessarily the page itself).