Theorems · Theorem · category theory
CategoryTheory.CatCenter.naturality
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (z : CategoryTheory.CatCenter C) {X Y : C} (f : X ⟶ Y),
CategoryTheory.CategoryStruct.comp f (z.app Y) = CategoryTheory.CategoryStruct.comp (z.app X) f- Defined in
- Mathlib.CategoryTheory.Center.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 17,999
- CategoryTheory.NatTrans.naturalityproof · cited by 318
- CategoryTheory.CatCenterstatement and proof · cited by 53
- CategoryTheory.CatCenter.appstatement · cited by 31
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.CatCenter.smul_iso_hom_eq'proof · cited by 1
- CategoryTheory.CatCenter.smul_iso_inv_eq'proof · cited by 1
- CategoryTheory.CatCenter.mul_appproof · cited by 1
- CategoryTheory.Linear.smulOfRingMorphism_smul_eq'proof · cited by 0
- CategoryTheory.CatCenter.naturality_assocproof · cited by 0
- CategoryTheory.CatCenter.smul_eq'proof · cited by 0