Theorems · Definition · category theory
CategoryTheory.ChosenPullbacks
(C : Type u₁) → [CategoryTheory.Category.{v₁, u₁} C] → Type (max u₁ v₁)A category has chosen pullbacks if every morphism has a chosen pullback.
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.Homproof · cited by 32,603
- CategoryTheory.ChosenPullbacksAlongproof · cited by 73
Cited by52
Results whose statement or proof uses this declaration.
- CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryOverstatement and proof · cited by 49
- CategoryTheory.toOverIteratedSliceForwardIsoPullbackstatement and proof · cited by 2
- CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fststatement and proof · cited by 1
- CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fststatement and proof · cited by 1
- CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_sndstatement and proof · cited by 1
- CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fststatement and proof · cited by 1
- CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_sndstatement and proof · cited by 1
- CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_sndstatement and proof · cited by 1
- CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fststatement and proof · cited by 1
- CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_sndstatement and proof · cited by 1
- CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fststatement and proof · cited by 1
- CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_sndstatement and proof · cited by 1