Mathlib Map

Theorems · Definition · group theory

MonoidHom.fst

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

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

Defined in
Mathlib.Algebra.Group.Prod
Cited by
28 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.

RingHom.fst · cited by 36RingHom.fstMonoidHom.prodMap · cited by 13MonoidHom.prodMapMonoidWithZeroHom.fst · cited by 10MonoidWithZeroHom.fstMulEquiv.prodUnits · cited by 7MulEquiv.prodUnitsMonoidHom.coprod · cited by 7MonoidHom.coprodSubgroup.goursatFst · cited by 6Subgroup.goursatFstSubgroup.goursatSnd · cited by 6Subgroup.goursatSndMonoidWithZeroHom.fst_inl · cited by 3MonoidWithZeroHom.fst_inlOrderMonoidHom.fst · cited by 3OrderMonoidHom.fstSubgroup.normal_goursatFst · cited by 3Subgroup.normal_goursatFstisCyclic_left_of_prod · cited by 2isCyclic_left_of_prodGrpCat.binaryProductLimitCone · cited by 2GrpCat.binaryProductLimit…CommGrpCat.binaryProductLimitCone · cited by 2CommGrpCat.binaryProductL…MonoidHom.fst_comp_prod · cited by 2MonoidHom.fst_comp_prodMonoidWithZeroHom.fst_comp_inr · cited by 1MonoidWithZeroHom.fst_com…MonoidHom · cited by 3629MonoidHomMulOneClass · cited by 1018MulOneClassMonoidHom.fstCITED BYCITES

Cites2

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

Cited by39

Results whose statement or proof uses this declaration.