Theorems · Definition · ring theory
Coalgebra.TensorProduct.lid
(R : Type u_5) →
(P : Type u_9) →
[inst : CommSemiring R] →
[inst_1 : AddCommMonoid P] → [inst_2 : Module R P] → [inst_3 : Coalgebra R P] → TensorProduct R R P ≃ₗc[R] PThe base ring is a left identity for the tensor product of coalgebras, up to coalgebra equivalence.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.idproof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearEquivproof · cited by 3,317
- TensorProductstatement and proof · cited by 2,545
- LinearEquiv.toLinearMapproof · cited by 1,171
- Coalgebrastatement and proof · cited by 112
- TensorProduct.lidproof · cited by 96
- CoalgEquivstatement · cited by 77
- LinearEquiv.invFunproof · cited by 29
Cited by6
Results whose statement or proof uses this declaration.
- Bialgebra.TensorProduct.lidproof · cited by 6
- CoalgCat.leftUnitor_defstatement · cited by 0
- Coalgebra.TensorProduct.lid_toLinearEquivstatement · cited by 0
- Coalgebra.TensorProduct.lid_symm_applystatement · cited by 0
- Coalgebra.TensorProduct.lid_tmulstatement · cited by 0
- Bialgebra.TensorProduct.lid_toCoalgEquivstatement · cited by 0