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Theorems · Theorem · category theory

ModuleCat.hom_ext

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

Around this declaration

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

groupCohomology.comp_d₁₂_eq · cited by 10groupCohomology.comp_d₁₂_…groupHomology.comp_d₂₁_eq · cited by 10groupHomology.comp_d₂₁_eqModuleCat.hom_ext_iff · cited by 10ModuleCat.hom_ext_iffgroupHomology.inhomogeneousChains.ext · cited by 8inhomogeneousChains.extgroupCohomology.comp_d₀₁_eq · cited by 6groupCohomology.comp_d₀₁_…groupHomology.comp_d₁₀_eq · cited by 6groupHomology.comp_d₁₀_eqgroupHomology.comp_d₃₂_eq · cited by 6groupHomology.comp_d₃₂_eqgroupCohomology.comp_d₂₃_eq · cited by 5groupCohomology.comp_d₂₃_…groupCohomology.cochainsMap_f_0_comp_cochainsIso₀ · cited by 4groupCohomology.cochainsM…groupCohomology.cochainsMap_f_2_comp_cochainsIso₂ · cited by 4groupCohomology.cochainsM…ModuleCat.ExtendScalars.hom_ext · cited by 4ExtendScalars.hom_extgroupCohomology.d₀₁_comp_d₁₂ · cited by 4groupCohomology.d₀₁_comp_…ModuleCat.MonoidalCategory.tensorμ_eq_tensorTensorTensorComm · cited by 4MonoidalCategory.tensorμ_…groupHomology.d₂₁_comp_d₁₀ · cited by 4groupHomology.d₂₁_comp_d₁₀groupCohomology.d₁₂_comp_d₂₃ · cited by 3groupCohomology.d₁₂_comp_…Quiver.Hom · cited by 32603Quiver.HomRingHom.id · cited by 18349RingHom.idLinearMap · cited by 10215LinearMapRing · cited by 7463RingModuleCat · cited by 1429ModuleCatModuleCat.carrier · cited by 997ModuleCat.carrierModuleCat.Hom.hom · cited by 341Hom.homModuleCat.Hom.ext · cited by 2Hom.extModuleCat.hom_extCITED BYCITES

Cites8

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Cited by84

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