Theorems · Theorem · ring theory

Pi.comul_single

∀ {R : Type u_1} {n : Type u_2} [inst : CommSemiring R] [inst_1 : Fintype n] [inst_2 : DecidableEq n] {A : n → Type u_3}
  [inst_3 : (i : n) → AddCommMonoid (A i)] [inst_4 : (i : n) → Module R (A i)]
  [inst_5 : (i : n) → CoalgebraStruct R (A i)] (i : n) (a : A i),
  CoalgebraStruct.comul (Pi.single i a) =
    (TensorProduct.map (LinearMap.single R A i) (LinearMap.single R A i)) (CoalgebraStruct.comul a)

Defined in

Mathlib.RingTheory.Coalgebra.Basic

Cited by

7 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringFintypeDecidableEqAddCommMonoidModuleCoalgebraStruct