Tom Leinster recently posed an interesting question in a talk at CLAP: “how do I generalize a theorem about objects into a theorem about maps?” The general idea comes from Grothendieck’s relative point of view, and to implement this point of view, one has to overcome certain technical hurdles related to “base change.” I thought I’d spend some time trying to lay out what it means to have a change of basis in algebraic geometry, and then how that idea shows up in Tom’s project: turning entropy into a functor.

You can read about Tom’s project (joint with John Baez and Tobiaz Fritz) directly here: https://ncatlab.org/johnbaez/show/Entropy+as+a+functor

(Currently writing this up, so excuse the notes below!)
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