[Merged by Bors] - feat(algebra/order/hom/monoid): add monotone_iff_map_nonneg/pos + golf
#16601
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…olf (#16601) If the source is an ordered add_group, a monoid hom is monotone if and only if it sends nonnegative elements to a nonnegative elements. This connects the notion of [positive linear functional](https://en.wikipedia.org/wiki/Positive_linear_functional) to monotonicity. [Zulip](https://leanprover.zulipchat.com/#narrow/stream/113489-new-members/topic/Amenable.20Groups/near/300076886)
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monotone_iff_map_nonneg/pos + golfmonotone_iff_map_nonneg/pos + golf
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If the source is an ordered add_group, a monoid hom is monotone if and only if it sends nonnegative elements to a nonnegative elements. This connects the notion of positive linear functional to monotonicity.
Zulip