Theorems · Definition · category theory
CategoryTheory.ChosenPullbacksAlong.comp
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{X Y Z : C} →
(f : X ⟶ Y) →
(g : Y ⟶ Z) →
[CategoryTheory.ChosenPullbacksAlong f] →
[CategoryTheory.ChosenPullbacksAlong g] →
CategoryTheory.ChosenPullbacksAlong (CategoryTheory.CategoryStruct.comp f g)The composition of morphisms with chosen pullbacks has a chosen pullback.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.Functor.compproof · cited by 6,529
- CategoryTheory.Iso.symmproof · cited by 993
- CategoryTheory.ChosenPullbacksAlongstatement and proof · cited by 73
- CategoryTheory.ChosenPullbacksAlong.pullbackproof · cited by 62
- CategoryTheory.Adjunction.compproof · cited by 42
- CategoryTheory.ChosenPullbacksAlong.mapPullbackAdjproof · cited by 29
- CategoryTheory.Adjunction.ofNatIsoLeftproof · cited by 10
- CategoryTheory.Over.mapCompproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.ChosenPullbacksAlong.unit_pullbackComp_homstatement · cited by 1
- CategoryTheory.ChosenPullbacksAlong.pullbackComp_hom_counitstatement · cited by 1
- CategoryTheory.ChosenPullbacksAlong.pullbackComp_hom_counit_assocstatement · cited by 0
- CategoryTheory.ChosenPullbacksAlong.unit_pullbackComp_hom_assocstatement · cited by 0