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Theorems · Theorem · category theory

CategoryTheory.eq_whisker

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} {f g : X ⟶ Y},
  f = g → ∀ (h : Y ⟶ Z), CategoryTheory.CategoryStruct.comp f h = CategoryTheory.CategoryStruct.comp g h

Postcompose an equation between morphisms by another morphism

Defined in
Mathlib.CategoryTheory.Category.Basic
Cited by
66 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
CategoryTheory.Category

Around this declaration

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

CategoryTheory.ShortComplex.exact_iff_exact_up_to_refinements · cited by 14ShortComplex.exact_iff_ex…CategoryTheory.Limits.ChosenPullback₃.w₃ · cited by 6ChosenPullback₃.w₃CategoryTheory.Limits.ChosenPullback₃.w₁ · cited by 5ChosenPullback₃.w₁CategoryTheory.Localization.SmallShiftedHom.equiv_mk₀Inv · cited by 4SmallShiftedHom.equiv_mk₀…HomotopicalAlgebra.RightHomotopyClass.precomp_bijective_of_cofibration_of_weakEquivalence · cited by 4RightHomotopyClass.precom…CategoryTheory.Abelian.SpectralObject.kernelSequenceE_exact · cited by 2SpectralObject.kernelSequ…CategoryTheory.Abelian.SpectralObject.cokernelSequenceE_exact · cited by 2SpectralObject.cokernelSe…CategoryTheory.PreOneHypercover.sieve₁_eq_pullback_sieve₁' · cited by 2PreOneHypercover.sieve₁_e…CategoryTheory.AddGrpObj.lift_neg_comp_left · cited by 2AddGrpObj.lift_neg_comp_l…CategoryTheory.AddGrpObj.lift_neg_comp_right · cited by 2AddGrpObj.lift_neg_comp_r…CategoryTheory.AddGrpObj.neg_hom · cited by 2AddGrpObj.neg_homCategoryTheory.ObjectProperty.IsCoseparating.mono_productTo · cited by 2IsCoseparating.mono_produ…CategoryTheory.finrank_hom_simple_simple_le_one · cited by 2CategoryTheory.finrank_ho…CategoryTheory.GrpObj.inv_hom · cited by 2GrpObj.inv_homCategoryTheory.GrpObj.lift_inv_comp_left · cited by 2GrpObj.lift_inv_comp_leftCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.eq_whiskerCITED BYCITES

Cites3

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Cited by66

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