Theorems · Theorem · category theory
TopCat.ext
∀ {X Y : TopCat} {f g : X ⟶ Y},
(∀ (x : ↑X), (CategoryTheory.ConcreteCategory.hom f) x = (CategoryTheory.ConcreteCategory.hom g) x) → f = g- Defined in
- Mathlib.Topology.Category.TopCat.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- TopCatstatement and proof · cited by 1,889
- CategoryTheory.ConcreteCategory.hom_extproof · cited by 48
Cited by10
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.homOfLE_baseproof · cited by 3
- TopCat.binaryCofan_isColimit_iffproof · cited by 1
- TopCat.Homotopy.ι₀_hproof · cited by 1
- TopCat.Homotopy.ι₁_hproof · cited by 1
- TopCat.Homotopy.h_compproof · cited by 0
- AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_facproof · cited by 0
- TopCat.ext_iffproof · cited by 0
- TopCat.of_homeoOfIsoproof · cited by 0
- AlgebraicGeometry.FormallyUnramified.hom_extproof · cited by 0
- AlgebraicGeometry.ΓSpec.right_triangleproof · cited by 0