Theorems · Theorem · category theory
CategoryTheory.Over.Hom.w
∀ {T : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} T] {X : T} {f g : CategoryTheory.Over X} (φ : f ⟶ g),
CategoryTheory.CategoryStruct.comp (CategoryTheory.Over.Hom.left φ) g.hom = f.hom- Defined in
- Mathlib.CategoryTheory.Comma.Over.Basic
- Cited by
- 12 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.Overstatement and proof · cited by 935
- CategoryTheory.Over.leftstatement · cited by 541
- CategoryTheory.Over.homstatement · cited by 370
- CategoryTheory.Over.Hom.leftstatement · cited by 287
- CategoryTheory.Over.wproof · cited by 42
Cited by12
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.exists_map_preimage_le_map_preimageproof · cited by 3
- CategoryTheory.MorphismProperty.overPullbackMapproof · cited by 2
- CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_fstproof · cited by 1
- CategoryTheory.Over.μ_pullback_left_fst_fstproof · cited by 1
- CategoryTheory.Over.μ_pullback_left_fst_sndproof · cited by 1
- CategoryTheory.Over.μ_pullback_left_sndproof · cited by 1
- CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_snd'proof · cited by 0
- CategoryTheory.Over.over_hasTerminalproof · cited by 0
- CategoryTheory.Over.prodComparisonIso_pullback_inv_left_snd'proof · cited by 0
- CategoryTheory.Over.lift_leftstatement · cited by 0
- CategoryTheory.Over.Hom.w_assocproof · cited by 0