Theorems · Inductive type · order theory

OrderMonoidHom

(α : Type u_6) → (β : Type u_7) → [Preorder α] → [Preorder β] → [MulOneClass α] → [MulOneClass β] → Type (max u_6 u_7)

α →*o β is the type of functions α → β that preserve the ordered monoid structure. OrderMonoidHom is also used for ordered group homomorphisms. When possible, instead of parametrizing results over (f : α →*o β), you should parametrize over (F : Type*) [FunLike F M N] [MonoidHomClass F M N] [OrderHomClass F M N] (f : F).

Defined in

Mathlib.Algebra.Order.Hom.Monoid

Cited by

67 results in Mathlib

Foundations

Depth 1 from the axioms · uses no axioms

Assumes

PreorderPreorderMulOneClassMulOneClass