Theorems · Theorem · group theory
FreeAbelianGroup.lift_comp_apply
∀ {α : Type u_2} {β : Type u_3} {γ : Type u_4} [inst : AddCommGroup β] [inst_1 : AddCommGroup γ]
(a : FreeAbelianGroup α) (f : α → β) (g : β →+ γ),
(FreeAbelianGroup.lift (⇑g ∘ f)) a = g ((FreeAbelianGroup.lift f) a)- Defined in
- Mathlib.GroupTheory.FreeAbelianGroup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupAddCommGroup
Around this declaration
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommGroupstatement and proof · cited by 12,871
- Equivstatement · cited by 8,337
- AddMonoidHomstatement and proof · cited by 3,230
- AddMonoidHom.compproof · cited by 339
- FreeAbelianGroupstatement and proof · cited by 82
- FreeAbelianGroup.liftstatement and proof · cited by 33
- FreeAbelianGroup.lift_apply_ofproof · cited by 12
- AddMonoidHom.comp_applyproof · cited by 12
- FreeAbelianGroup.lift_uniqueproof · cited by 3
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