Mathlib Map

Theorems · Definition · group theory

MulHom.prodMap

{M : Type u_3} →
  {N : Type u_4} →
    {M' : Type u_6} →
      {N' : Type u_7} →
        [inst : Mul M] →
          [inst_1 : Mul N] → [inst_2 : Mul M'] → [inst_3 : Mul N'] → (M →ₙ* M') → (N →ₙ* N') → M × N →ₙ* M' × N'

Prod.map as a MonoidHom.

Defined in
Mathlib.Algebra.Group.Prod
Cited by
4 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext
Assumes
MulMulMulMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

MulHom.prod_map_comap_prod' · cited by 0MulHom.prod_map_comap_pro…MulHom.coe_prodMap · cited by 0MulHom.coe_prodMapMulHom.prodMap_def · cited by 0MulHom.prodMap_defMulHom.prod_comp_prodMap · cited by 0MulHom.prod_comp_prodMapMulHom · cited by 299MulHomMulHom.comp · cited by 44MulHom.compMulHom.snd · cited by 9MulHom.sndMulHom.fst · cited by 8MulHom.fstMulHom.prod · cited by 7MulHom.prodMulHom.prodMapCITED BYCITES

Cites5

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

Cited by4

Results whose statement or proof uses this declaration.