Theorems · Definition · ring theory
CoalgebraStruct.comul
{R : Type u} →
{A : Type v} →
{inst : CommSemiring R} →
{inst_1 : AddCommMonoid A} → {inst_2 : Module R A} → [self : CoalgebraStruct R A] → A →ₗ[R] TensorProduct R A AThe comultiplication of the coalgebra
- Defined in
- Mathlib.RingTheory.Coalgebra.Basic
- Cited by
- 118 results in Mathlib
- Foundations
- Depth 56 from the axioms, rests on 836 definitions · uses propext, Quot.sound
- Assumes
- CoalgebraStruct
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- TensorProductstatement · cited by 2,545
- CoalgebraStructstatement and proof · cited by 230
Cited by157
Results whose statement or proof uses this declaration.
- Bialgebra.comulAlgHomproof · cited by 20
- IsGroupLikeElem.comul_eq_tmul_selfstatement · cited by 13
- Coalgebra.Repr.eqstatement · cited by 7
- Pi.comul_singlestatement and proof · cited by 7
- Bialgebra.comul_onestatement · cited by 6
- Finsupp.comul_singlestatement and proof · cited by 5
- CoalgHomClass.map_comp_comulstatement · cited by 4
- Coalgebra.rTensor_counit_comp_comulstatement · cited by 4
- CoalgCat.ofComonObjCoalgebraStruct_comulstatement and proof · cited by 4
- Bialgebra.comulAlgHom_applystatement · cited by 4
- AddMonoidAlgebra.comul_singlestatement and proof · cited by 4
- Coalgebra.coassocstatement · cited by 3