Theorems · Definition · category theory
CategoryTheory.CatCenter.app
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.CatCenter C → (X : C) → X ⟶ XThe action of the center of a category on an object. (This is necessary as
NatTrans.app x X is syntactically an endomorphism of (𝟭 C).obj X
rather than of X.)
- Defined in
- Mathlib.CategoryTheory.Center.Basic
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 21 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.
Cites4
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 · cited by 32,603
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.CatCenterstatement and proof · cited by 53
Cited by37
Results whose statement or proof uses this declaration.
- CategoryTheory.CatCenter.naturalitystatement · cited by 6
- CategoryTheory.CatCenter.localization_appstatement and proof · cited by 5
- CategoryTheory.CatCenter.ext_of_localizationstatement and proof · cited by 4
- CategoryTheory.Linear.smulOfRingMorphismproof · cited by 2
- CategoryTheory.CatCenter.mul_app'statement · cited by 2
- CategoryTheory.CatCenter.smul_iso_hom_eq'statement · cited by 1
- CategoryTheory.CatCenter.smul_iso_inv_eqstatement · cited by 1
- CategoryTheory.CatCenter.smul_iso_inv_eq'statement · cited by 1
- CategoryTheory.Functor.commShift₂_commstatement · cited by 1
- CategoryTheory.Functor.CommShift₂.commstatement · cited by 1
- CategoryTheory.Linear.smulOfRingMorphism_smul_eqstatement · cited by 1
- CategoryTheory.CatCenter.extstatement and proof · cited by 1