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