Theorems · Theorem · category theory
CategoryTheory.CostructuredArrow.w
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{S : CategoryTheory.Functor C D} {T : D} {X Y : CategoryTheory.CostructuredArrow S T} (f : X ⟶ Y),
CategoryTheory.CategoryStruct.comp (S.map f.left) Y.hom = X.hom- Cited by
- 10 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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 · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement · cited by 8,698
- CategoryTheory.Discretestatement · cited by 2,447
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Comma.leftstatement · cited by 886
- CategoryTheory.Functor.fromPUnitstatement · cited by 769
- CategoryTheory.CostructuredArrowstatement and proof · cited by 536
- CategoryTheory.CommaMorphism.leftstatement · cited by 526
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.CostructuredArrow.Hom.wproof · cited by 1
- CategoryTheory.Bicategory.RightLift.wproof · cited by 1
- CategoryTheory.CostructuredArrow.homMk_surjectiveproof · cited by 1
- CategoryTheory.CostructuredArrow.w_prod_fstproof · cited by 1
- CategoryTheory.CostructuredArrow.w_prod_sndproof · cited by 1
- CategoryTheory.exists_eq_of_isCofiltered_costructuredArrowproof · cited by 1
- CategoryTheory.Functor.bijective_sectionsPrecompproof · cited by 1
- CategoryTheory.Bicategory.RightExtension.wproof · cited by 1
- CategoryTheory.CostructuredArrow.w_assocproof · cited by 0