slightly silly observation: if your category has products you can write the group axioms in them by pretending it's the category of sets
is this true for any FOL structure or am I missing something?
I think it's true for any FOL structure
is there anything nontrivial here? I guess we are now allowed to write "topological" before anything in FOL and have it make sense
similarly things with some kind of symmetry
I don't know enough category theory and am a bear of v little brain
ok i guess we may need coproducts as well to express disjunctions
"either x has a multiplicative inverse or x is 0"
not sure the reals are a "topological field" in this sense though
or we have to settle for a rather more resticted set of FOL objects