Mathlib Map

Theorems · Definition · group theory

FreeAddGroup.map

{α : Type u} → {β : Type v} → (α → β) → FreeAddGroup α →+ FreeAddGroup β

Any function from α to β extends uniquely to an additive group homomorphism from the additive free group over α to the additive free group over β.

Defined in
Mathlib.GroupTheory.FreeGroup.Basic
Cited by
16 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FreeAddGroup.freeAddGroupCongr · cited by 5FreeAddGroup.freeAddGroup…FreeAddGroup.map.id · cited by 3map.idFreeAddGroup.map.comp · cited by 2map.compFreeAddGroup.map.of · cited by 1map.ofFreeAddGroup.map_eq_lift · cited by 1FreeAddGroup.map_eq_liftFreeAddGroup.map_injective · cited by 1FreeAddGroup.map_injectiveFreeAddGroup.map_surjective · cited by 1FreeAddGroup.map_surjecti…FreeAddGroup.range_map · cited by 1FreeAddGroup.range_mapFreeAddGroup.lift_eq_sum_map · cited by 0FreeAddGroup.lift_eq_sum_…FreeAddGroup.map.id' · cited by 0map.id'FreeAddGroup.map.mk · cited by 0map.mkFreeAddGroup.map.unique · cited by 0map.uniqueFreeAddGroup.map_add · cited by 0FreeAddGroup.map_addFreeAddGroup.map_bijective · cited by 0FreeAddGroup.map_bijectiveFreeAddGroup.map_neg · cited by 0FreeAddGroup.map_negAddMonoidHom · cited by 3230AddMonoidHomFreeAddGroup · cited by 90FreeAddGroupFreeAddGroup.Red.Step · cited by 41Red.StepAddMonoidHom.mk' · cited by 25AddMonoidHom.mk'Quot.map · cited by 5Quot.mapFreeAddGroup.mapCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by18

Results whose statement or proof uses this declaration.