Theorems · Definition · ring theory
Coalgebra.Repr.left
{R : Type u} →
{A : Type v} →
[inst : CommSemiring R] →
[inst_1 : AddCommMonoid A] →
[inst_2 : Module R A] → [inst_3 : CoalgebraStruct R A] → {a : A} → {ι : Type u_1} → Coalgebra.Repr R a ι → ι → Athe first coordinate of a representation of comul a
- Defined in
- Mathlib.RingTheory.Coalgebra.Basic
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- CoalgebraStructstatement and proof · cited by 230
- Coalgebra.Reprstatement and proof · cited by 25
Cited by23
Results whose statement or proof uses this declaration.
- Coalgebra.Repr.eqstatement · cited by 7
- Coalgebra.Repr.tmulproof · cited by 4
- Coalgebra.Repr.inducedproof · cited by 3
- HopfAlgebra.sum_antipode_mul_eq_algebraMap_counitstatement and proof · cited by 3
- HopfAlgebra.sum_mul_antipode_eq_algebraMap_counitstatement and proof · cited by 3
- Coalgebra.Repr.convMul_applystatement and proof · cited by 3
- Coalgebra.sum_counit_tmul_eqstatement and proof · cited by 2
- Coalgebra.Repr.mul_leftstatement and proof · cited by 1
- HopfAlgebra.antipode_comp_mul_comp_commproof · cited by 1
- Coalgebra.sum_counit_smulstatement and proof · cited by 1
- Coalgebra.sum_tmul_counit_eqstatement and proof · cited by 1
- Coalgebra.sum_tmul_tmul_eqstatement and proof · cited by 1