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 hPostcompose 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
Cited by66
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.exact_iff_exact_up_to_refinementsproof · cited by 14
- CategoryTheory.Limits.ChosenPullback₃.w₃proof · cited by 6
- CategoryTheory.Limits.ChosenPullback₃.w₁proof · cited by 5
- CategoryTheory.Localization.SmallShiftedHom.equiv_mk₀Invproof · cited by 4
- CategoryTheory.Abelian.SpectralObject.kernelSequenceE_exactproof · cited by 2
- CategoryTheory.Abelian.SpectralObject.cokernelSequenceE_exactproof · cited by 2
- CategoryTheory.PreOneHypercover.sieve₁_eq_pullback_sieve₁'proof · cited by 2
- CategoryTheory.AddGrpObj.lift_neg_comp_leftproof · cited by 2
- CategoryTheory.AddGrpObj.lift_neg_comp_rightproof · cited by 2
- CategoryTheory.AddGrpObj.neg_homproof · cited by 2
- CategoryTheory.ObjectProperty.IsCoseparating.mono_productToproof · cited by 2