Theorems · Theorem · commutative algebra
TensorProduct.map_id
∀ {R : Type u_1} [inst : CommSemiring R] {M : Type u_7} {N : Type u_8} [inst_1 : AddCommMonoid M]
[inst_2 : AddCommMonoid N] [inst_3 : Module R M] [inst_4 : Module R N],
TensorProduct.map LinearMap.id LinearMap.id = LinearMap.id- Defined in
- Mathlib.LinearAlgebra.TensorProduct.Map
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 62 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.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
- TensorProduct.tmulproof · cited by 1,182
- LinearMap.extproof · cited by 844
- LinearMap.idstatement · cited by 625
- TensorProduct.mapstatement · cited by 250
- TensorProduct.extproof · cited by 50
Cited by16
Results whose statement or proof uses this declaration.
- LinearMap.lTensor_idproof · cited by 8
- LinearMap.rTensor_idproof · cited by 5
- CoassocSimps.assoc_comp_mapproof · cited by 4
- CoassocSimps.assoc_symm_comp_mapproof · cited by 3
- TensorProduct.map_oneproof · cited by 1
- CoassocSimps.coassoc_rightproof · cited by 1
- CoassocSimps.coassoc_leftproof · cited by 1
- CoassocSimps.assoc_comp_map_comm_comp_comul_comp_comul_assocproof · cited by 0
- DFinsupp.comul_comp_lapplyproof · cited by 0
- Finsupp.comul_comp_lapplyproof · cited by 0
- Prod.comul_comp_fstproof · cited by 0
- Prod.comul_comp_sndproof · cited by 0