Theorems · Theorem · category theory
CategoryTheory.NatTrans.ext
∀ {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} {x y : CategoryTheory.NatTrans F G}, x.app = y.app → x = y- Defined in
- Mathlib.CategoryTheory.NatTrans
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
- CategoryTheory.NatTransstatement and proof · cited by 82
Cited by20
Results whose statement or proof uses this declaration.
- CategoryTheory.NatTrans.ext'proof · cited by 340
- CategoryTheory.TwoSquare.extproof · cited by 15
- TopCat.Presheaf.extproof · cited by 11
- CategoryTheory.SimplicialObject.hom_extproof · cited by 4
- CategoryTheory.NatTrans.ext_iffproof · cited by 2
- SSet.Truncated.hom_extproof · cited by 2
- AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_eqproof · cited by 1
- CategoryTheory.yonedaPairingExtproof · cited by 1
- CategoryTheory.CosimplicialObject.hom_extproof · cited by 1
- CategoryTheory.presheafHom_isSheafForproof · cited by 1
- CategoryTheory.coyonedaPairingExtproof · cited by 1