Theorems · Theorem · linear algebra

homTensorHomEquiv_toLinearMap

∀ (R : Type u_2) (M : Type u_3) (N : Type u_4) (P : Type u_5) (Q : Type u_6) [inst : CommSemiring R]
  [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid N] [inst_3 : AddCommMonoid P] [inst_4 : AddCommMonoid Q]
  [inst_5 : Module R M] [inst_6 : Module R N] [inst_7 : Module R P] [inst_8 : Module R Q]
  [inst_9 : Module.Projective R M] [inst_10 : Module.Finite R M] [inst_11 : Module.Projective R N]
  [inst_12 : Module.Finite R N], ↑(homTensorHomEquiv R M N P Q) = TensorProduct.homTensorHomMap (RingHom.id R) M N P Q

Defined in: Mathlib.LinearAlgebra.Contraction
Cited by: 1 results in Mathlib
Foundations: Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring AddCommMonoid AddCommMonoid AddCommMonoid AddCommMonoid Module Module Module Module Module.Projective Module.Finite Module.Projective Module.Finite

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Cites26

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
LinearMapstatement and proof · cited by 10,215
TensorProductstatement and proof · cited by 2,545
TensorProduct.tmulproof · cited by 1,182
LinearEquiv.toLinearMapstatement and proof · cited by 1,171
Module.Finitestatement and proof · cited by 1,032
LinearMap.extproof · cited by 844
LinearEquiv.reflproof · cited by 143

Cited by1

Results whose statement or proof uses this declaration.

homTensorHomEquiv_applyproof · cited by 0