Theorems · Definition · category theory
CategoryTheory.NatTrans.app
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{D : Type u₂} →
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
{F G : CategoryTheory.Functor C D} → CategoryTheory.NatTrans F G → (X : C) → F.obj X ⟶ G.obj XThe component of a natural transformation.
- Defined in
- Mathlib.CategoryTheory.NatTrans
- Cited by
- 7,406 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 10 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.NatTransstatement and proof · cited by 82
Cited by8,556
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.whiskerLeftproof · cited by 496
- CategoryTheory.Functor.whiskerRightproof · cited by 467
- CategoryTheory.Limits.colimit.ιproof · cited by 397
- CategoryTheory.Functor.whiskeringLeftproof · cited by 395
- CategoryTheory.NatTrans.ext'statement and proof · cited by 340
- CategoryTheory.Functor.flipproof · cited by 320
- CategoryTheory.NatTrans.naturalitystatement · cited by 318
- CategoryTheory.Limits.limit.πproof · cited by 278
- CategoryTheory.Limits.limit.lift_πstatement · cited by 266
- CategoryTheory.Iso.appproof · cited by 253
- CategoryTheory.Functor.whiskeringRightproof · cited by 221
- CategoryTheory.Adjunction.homEquivproof · cited by 202
Showing the 200 most cited of 8,556.