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Theorems · Definition · category theory

CategoryTheory.Limits.pullback.cone

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y Z : C} →
      (f : X ⟶ Z) → (g : Y ⟶ Z) → [CategoryTheory.Limits.HasPullback f g] → CategoryTheory.Limits.PullbackCone f g

The cone associated to the pullback of f and g

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
Cited by
18 results in Mathlib
Foundations
Depth 18 from the axioms · uses Classical.choice
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasPullback

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Over.cartesianMonoidalCategory · cited by 68Over.cartesianMonoidalCat…CategoryTheory.Limits.pullback.isLimit · cited by 24pullback.isLimitCategoryTheory.Over.whiskerLeft_left_snd · cited by 2Over.whiskerLeft_left_sndCategoryTheory.Over.whiskerRight_left_fst · cited by 2Over.whiskerRight_left_fstCategoryTheory.Over.whiskerRight_left_snd · cited by 2Over.whiskerRight_left_sndCategoryTheory.Over.whiskerLeft_left_fst · cited by 2Over.whiskerLeft_left_fstCategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_fst · cited by 1Over.prodComparisonIso_pu…CategoryTheory.Over.μ_pullback_left_fst_fst · cited by 1Over.μ_pullback_left_fst_…CategoryTheory.Over.μ_pullback_left_fst_snd · cited by 1Over.μ_pullback_left_fst_…CategoryTheory.IsUniversalColimit.nonempty_isColimit_prod_of_pullbackCone · cited by 1IsUniversalColimit.nonemp…CategoryTheory.Over.associator_hom_left_fst · cited by 1Over.associator_hom_left_…CategoryTheory.Over.associator_hom_left_snd_fst · cited by 1Over.associator_hom_left_…CategoryTheory.Over.associator_hom_left_snd_snd · cited by 1Over.associator_hom_left_…CategoryTheory.Over.associator_inv_left_fst_fst · cited by 1Over.associator_inv_left_…CategoryTheory.Over.associator_inv_left_fst_snd · cited by 1Over.associator_inv_left_…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.cospan · cited by 467Limits.cospanCategoryTheory.Limits.HasPullback · cited by 434Limits.HasPullbackCategoryTheory.Limits.PullbackCone · cited by 136Limits.PullbackConeCategoryTheory.Limits.limit.cone · cited by 97limit.conepullback.coneCITED BYCITES

Cites6

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

Cited by20

Results whose statement or proof uses this declaration.