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Theorems · Theorem · category theory

SemimoduleCat.hom_ext

∀ {R : Type u} [inst : Semiring R] {M N : SemimoduleCat R} {f g : M ⟶ N},
  SemimoduleCat.Hom.hom f = SemimoduleCat.Hom.hom g → f = g
Defined in
Mathlib.Algebra.Category.ModuleCat.Semi
Cited by
15 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Quot.sound
Assumes
Semiring

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SemimoduleCat.MonoidalCategory.braiding_naturality · cited by 2MonoidalCategory.braiding…SemimoduleCat.isZero_of_subsingleton · cited by 1SemimoduleCat.isZero_of_s…SemimoduleCat.MonoidalCategory.tensor_ext₃' · cited by 1MonoidalCategory.tensor_e…SemimoduleCat.hom_ext_iff · cited by 0SemimoduleCat.hom_ext_iffSemimoduleCat.MonoidalCategory.leftUnitor_naturality · cited by 0MonoidalCategory.leftUnit…SemimoduleCat.MonoidalCategory.pentagon · cited by 0MonoidalCategory.pentagonSemimoduleCat.MonoidalCategory.triangle · cited by 0MonoidalCategory.triangleSemimoduleCat.MonoidalCategory.rightUnitor_naturality · cited by 0MonoidalCategory.rightUni…SemimoduleCat.MonoidalCategory.tensorHom_comp_tensorHom · cited by 0MonoidalCategory.tensorHo…SemimoduleCat.MonoidalCategory.tensor_ext · cited by 0MonoidalCategory.tensor_e…SemimoduleCat.MonoidalCategory.associator_naturality · cited by 0MonoidalCategory.associat…SemimoduleCat.MonoidalCategory.tensorμ_eq_tensorTensorTensorComm · cited by 0MonoidalCategory.tensorμ_…SemimoduleCat.MonoidalCategory.hexagon_forward · cited by 0MonoidalCategory.hexagon_…SemimoduleCat.MonoidalCategory.hexagon_reverse · cited by 0MonoidalCategory.hexagon_…SemimoduleCat.MonoidalCategory.id_tensorHom_id · cited by 0MonoidalCategory.id_tenso…Quiver.Hom · cited by 32603Quiver.HomRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringLinearMap · cited by 10215LinearMapSemimoduleCat · cited by 108SemimoduleCatSemimoduleCat.carrier · cited by 87SemimoduleCat.carrierSemimoduleCat.Hom.hom · cited by 45Hom.homSemimoduleCat.Hom.ext · cited by 2Hom.extSemimoduleCat.hom_extCITED BYCITES

Cites8

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Cited by15

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