Theorems · Definition · order theory

OrderMonoidHomClass.toOrderAddMonoidHom

{F : Type u_1} →
  {α : Type u_2} →
    {β : Type u_3} →
      [inst : Preorder α] →
        [inst_1 : Preorder β] →
          [inst_2 : AddZeroClass α] →
            [inst_3 : AddZeroClass β] →
              [inst_4 : FunLike F α β] → [OrderHomClass F α β] → [AddMonoidHomClass F α β] → F → α →+o β

Turn an element of a type F satisfying OrderHomClass F α β and AddMonoidHomClass F α β into an actual OrderAddMonoidHom. This is declared as the default coercion from F to α →+o β.

Defined in

Mathlib.Algebra.Order.Hom.Monoid

Cited by

5 results in Mathlib

Foundations

Depth 8 from the axioms · uses no axioms

Assumes

PreorderPreorderAddZeroClassAddZeroClassFunLikeOrderHomClassAddMonoidHomClass