Theorems · Inductive type · order theory

OrderAddMonoidHom

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

α →+o β is the type of monotone functions α → β that preserve the ordered additive monoid structure. OrderAddMonoidHom 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

80 results in Mathlib

Foundations

Depth 1 from the axioms · uses no axioms

Assumes

PreorderPreorderAddZeroClassAddZeroClass