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Oct 14 at 23:07 comment added sl_09 I guess the sort of functor you would like would send a vector space to its associated projective geometry viewed as a $K$-module. The issue is that this isn't obviously functorial. I think the naive definition is not functorial (I haven't checked carefully though). I don't have a great intuition for these sorts of things myself.
Oct 14 at 22:42 comment added Jonathan Beardsley But presumably this functor is not -⊗K...?
Oct 14 at 22:37 vote accept Jonathan Beardsley
Oct 14 at 22:36 comment added Jonathan Beardsley Ah thanks very much! Do you have any sense of how we are supposed to think about the relationship between vector spaces and combinatorial geometries? I guess there is a functor from vector spaces over a field 𝔽 to K-modules?
S Oct 14 at 22:26 review First answers
Oct 14 at 23:06
S Oct 14 at 22:26 history answered sl_09 CC BY-SA 4.0