Theorems · Definition · ring theory

BialgHom.comp

{R : Type u_1} →
  {A : Type u_2} →
    {B : Type u_3} →
      {C : Type u_4} →
        [inst : CommSemiring R] →
          [inst_1 : Semiring A] →
            [inst_2 : Semiring B] →
              [inst_3 : Semiring C] →
                [inst_4 : Algebra R A] →
                  [inst_5 : Algebra R B] →
                    [inst_6 : Algebra R C] →
                      [inst_7 : CoalgebraStruct R A] →
                        [inst_8 : CoalgebraStruct R B] →
                          [inst_9 : CoalgebraStruct R C] → (B →ₐc[R] C) → (A →ₐc[R] B) → A →ₐc[R] C

Composition of bialgebra homomorphisms.

Defined in

Mathlib.RingTheory.Bialgebra.Hom

Cited by

26 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringSemiringAlgebraAlgebraAlgebraCoalgebraStructCoalgebraStructCoalgebraStruct