Theorems · Theorem · category theory
CategoryTheory.Under.Hom.w
∀ {T : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} T] {X : T} {f g : CategoryTheory.Under X} (φ : f ⟶ g),
CategoryTheory.CategoryStruct.comp f.hom (CategoryTheory.Under.Hom.right φ) = g.hom- Defined in
- Mathlib.CategoryTheory.Comma.Over.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 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.
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.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Understatement and proof · cited by 276
- CategoryTheory.Under.rightstatement · cited by 128
- CategoryTheory.Under.homstatement · cited by 73
- CategoryTheory.Under.Hom.rightstatement · cited by 67
- CategoryTheory.Under.wproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.underPushoutMapproof · cited by 1
- CategoryTheory.Under.Hom.w_assocproof · cited by 0