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
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@alexthecamel First order logic structures in general requires toposes, not just products. However, it is true for any algebraic structure (monoids, groups, rings, ... BUT NOT fields because fields aren't a true algebraic structure due to having a != 0 condition on division).
