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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.

Defined in
Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong
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.

CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryOver · cited by 49ChosenPullbacksAlong.cart…CategoryTheory.toOverIteratedSliceForwardIsoPullback · cited by 2CategoryTheory.toOverIter…CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst · cited by 1Over.associator_hom_left_…CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst · cited by 1Over.associator_hom_left_…CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd · cited by 1Over.associator_hom_left_…CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst · cited by 1Over.associator_inv_left_…CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd · cited by 1Over.associator_inv_left_…CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd · cited by 1Over.associator_inv_left_…CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst · cited by 1Over.leftUnitor_inv_left_…CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd · cited by 1Over.leftUnitor_inv_left_…CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst · cited by 1Over.rightUnitor_inv_left…CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd · cited by 1Over.rightUnitor_inv_left…CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst · cited by 1Over.tensorHom_left_fstCategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd · cited by 1Over.tensorHom_left_sndCategoryTheory.ChosenPullbacksAlong.Over.tensorObj_ext · cited by 1Over.tensorObj_extCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.ChosenPullbacksAlong · cited by 73CategoryTheory.ChosenPull…CategoryTheory.ChosenPullbacksCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by52

Results whose statement or proof uses this declaration.