Theorems · Definition · group theory

DistribMulActionHom.comp

{M : Type u_1} →
  [inst : Monoid M] →
    {N : Type u_2} →
      [inst_1 : Monoid N] →
        {P : Type u_3} →
          [inst_2 : Monoid P] →
            {φ : M →* N} →
              {ψ : N →* P} →
                {χ : M →* P} →
                  {A : Type u_4} →
                    [inst_3 : AddMonoid A] →
                      [inst_4 : DistribMulAction M A] →
                        {B : Type u_5} →
                          [inst_5 : AddMonoid B] →
                            [inst_6 : DistribMulAction N B] →
                              {C : Type u_7} →
                                [inst_7 : AddMonoid C] →
                                  [inst_8 : DistribMulAction P C] →
                                    [κ : φ.CompTriple ψ χ] → (B →ₑ+[ψ] C) → (A →ₑ+[φ] B) → A →ₑ+[χ] C

Composition of two equivariant additive monoid homomorphisms.

Defined in

Mathlib.GroupTheory.GroupAction.Hom

Cited by

13 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Quot.sound

Assumes

MonoidMonoidMonoidAddMonoidDistribMulActionAddMonoidDistribMulActionAddMonoidDistribMulActionMonoidHom.CompTriple