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Theorems · Definition · group theory

AddMonoid.Coprod.mk

{M : Type u_1} →
  {N : Type u_2} → [inst : AddZeroClass M] → [inst_1 : AddZeroClass N] → FreeAddMonoid (M ⊕ N) →+ AddMonoid.Coprod M N

The natural projection FreeAddMonoid (M ⊕ N) →+ AddMonoid.Coprod M N.

Defined in
Mathlib.GroupTheory.Coprod.Basic
Cited by
16 results in Mathlib
Foundations
Depth 44 from the axioms · uses propext, Quot.sound
Assumes
AddZeroClassAddZeroClass
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Around this declaration

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

AddMonoid.Coprod.inl · cited by 42Coprod.inlAddMonoid.Coprod.inr · cited by 42Coprod.inrAddMonoid.Coprod.swap · cited by 25Coprod.swapAddMonoid.Coprod.map · cited by 12Coprod.mapAddMonoid.Coprod.mclosure_range_inl_union_inr · cited by 3Coprod.mclosure_range_inl…AddMonoid.Coprod.mk_eq_mk · cited by 1Coprod.mk_eq_mkAddMonoid.Coprod.mk_of_neg_add · cited by 1Coprod.mk_of_neg_addAddMonoid.Coprod.mk_surjective · cited by 1Coprod.mk_surjectiveAddMonoid.Coprod.mrange_mk · cited by 1Coprod.mrange_mkAddMonoid.Coprod.induction_on' · cited by 1Coprod.induction_on'AddMonoid.Coprod.lift_apply_mk · cited by 0Coprod.lift_apply_mkAddMonoid.Coprod.map_mk_ofList · cited by 0Coprod.map_mk_ofListAddMonoid.Coprod.mk_of_inl · cited by 0Coprod.mk_of_inlAddMonoid.Coprod.mk_of_inr · cited by 0Coprod.mk_of_inrAddMonoid.Coprod.clift_apply_mk · cited by 0Coprod.clift_apply_mkAddMonoidHom · cited by 3230AddMonoidHomAddZeroClass · cited by 1237AddZeroClassFreeAddMonoid · cited by 145FreeAddMonoidAddMonoid.Coprod · cited by 104AddMonoid.CoprodAddCon.mk' · cited by 21AddCon.mk'AddMonoid.coprodCon · cited by 3AddMonoid.coprodConCoprod.mkCITED BYCITES

Cites6

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

Cited by20

Results whose statement or proof uses this declaration.