Theorems · Definition · order theory

MulArchimedeanClass.orderHom

{M : Type u_1} →
  [inst : CommGroup M] →
    [inst_1 : LinearOrder M] →
      [inst_2 : IsOrderedMonoid M] →
        {N : Type u_2} →
          [inst_3 : CommGroup N] →
            [inst_4 : LinearOrder N] →
              [inst_5 : IsOrderedMonoid N] → (M →*o N) → MulArchimedeanClass M →o MulArchimedeanClass N

An OrderMonoidHom can be lifted to an OrderHom over archimedean classes.

Defined in

Mathlib.Algebra.Order.Archimedean.Class

Cited by

5 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupLinearOrderIsOrderedMonoidCommGroupLinearOrderIsOrderedMonoid