Theorems · Theorem · category theory
CategoryTheory.whisker_eq
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} {f g : Y ⟶ X} (h : Z ⟶ Y),
f = g → CategoryTheory.CategoryStruct.comp h f = CategoryTheory.CategoryStruct.comp h gPrecompose an equation between morphisms by another morphism
- Defined in
- Mathlib.CategoryTheory.Category.Basic
- Cited by
- 46 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 by46
Results whose statement or proof uses this declaration.
- CategoryTheory.GrpObj.lift_comp_inv_leftproof · cited by 6
- CategoryTheory.GrpObj.lift_comp_inv_rightproof · cited by 6
- CategoryTheory.AddGrpObj.lift_comp_neg_leftproof · cited by 6
- CategoryTheory.AddGrpObj.lift_comp_neg_rightproof · cited by 6
- CategoryTheory.MonObj.lift_comp_one_rightproof · cited by 5
- CategoryTheory.AddMonObj.lift_lift_assocproof · cited by 5
- CategoryTheory.AddMonObj.lift_comp_zero_rightproof · cited by 5
- CategoryTheory.MonObj.lift_comp_one_leftproof · cited by 4
- CategoryTheory.MonObj.lift_lift_assocproof · cited by 4
- CategoryTheory.AddMonObj.lift_comp_zero_leftproof · cited by 4
- CategoryTheory.Limits.chosenCoend.hom_extproof · cited by 3