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Sep 10, 2018 at 5:42 comment added R. van Dobben de Bruyn I'm unconvinced that a functor is the right thing to look for. Many analogies in mathematics are either linked by a larger generality that encompasses both (e.g. Galois groups and fundamental groups, linked many decades later by the étale fundamental group), or remain analogies forever (e.g. between proper curves over finite fields and number fields with their archimedean and non-archimedean places). I think it would be much more fruitful to look for a 'generalised geometric theory' that allows both as a special case.
Sep 9, 2018 at 22:24 history asked cll CC BY-SA 4.0