Mathlib Map

Theorems · Definition · group theory

MonoidHom.inl

(M : Type u_3) → (N : Type u_4) → [inst : MulOneClass M] → [inst_1 : MulOneClass N] → M →* M × N

Given monoids M, N, the natural inclusion homomorphism from M to M × N.

Defined in
Mathlib.Algebra.Group.Prod
Cited by
32 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
MulOneClassMulOneClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Localization.monoidOf · cited by 17Localization.monoidOfMonoidWithZeroHom.inl · cited by 13MonoidWithZeroHom.inlMonoid.Coprod.toProd · cited by 11Coprod.toProdOrderMonoidHom.inl · cited by 5OrderMonoidHom.inlSubmonoid.prod_le_iff · cited by 4Submonoid.prod_le_iffMonoidWithZeroHom.fst_inl · cited by 3MonoidWithZeroHom.fst_inlMonoidHom.commute_inl_inr · cited by 2MonoidHom.commute_inl_inrMonoidWithZeroHom.inl_apply_unit · cited by 2MonoidWithZeroHom.inl_app…Subgroup.prod_le_iff · cited by 2Subgroup.prod_le_iffSubmonoid.mrange_inl · cited by 2Submonoid.mrange_inlMonoidHom.mker_inl · cited by 1MonoidHom.mker_inlMonoidHom.inl_mono · cited by 1MonoidHom.inl_monoSubmonoid.map_inl · cited by 1Submonoid.map_inlSubmonoid.closure_one_prod · cited by 1Submonoid.closure_one_prodSubmonoid.closure_prod_one · cited by 1Submonoid.closure_prod_oneMonoidHom · cited by 3629MonoidHomMulOneClass · cited by 1018MulOneClassMonoidHom.inlCITED BYCITES

Cites2

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

Cited by38

Results whose statement or proof uses this declaration.