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Theorems · Definition · category theory

CategoryTheory.Limits.WidePullback.base

{J : Type w} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      {B : C} →
        {objs : J → C} →
          (arrows : (j : J) → objs j ⟶ B) →
            [inst_1 : CategoryTheory.Limits.HasWidePullback B objs arrows] →
              CategoryTheory.Limits.widePullback B objs arrows ⟶ B

The unique map to the base from the pullback.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks
Cited by
20 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasWidePullback

Around this declaration

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

CategoryTheory.Arrow.cechNerve · cited by 18Arrow.cechNerveCategoryTheory.Arrow.augmentedCechNerve · cited by 16Arrow.augmentedCechNerveCategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s · cited by 6ExtraDegeneracy.sCategoryTheory.Arrow.mapCechNerve · cited by 3Arrow.mapCechNerveCategoryTheory.Limits.WidePullback.lift_base · cited by 2WidePullback.lift_baseCategoryTheory.Limits.WidePullback.π_arrow · cited by 2WidePullback.π_arrowCategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_base · cited by 1ExtraDegeneracy.s_comp_ba…CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_π_0 · cited by 1ExtraDegeneracy.s_comp_π_0CategoryTheory.Limits.Concrete.widePullback_ext · cited by 1Concrete.widePullback_extCategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_π_succ · cited by 1ExtraDegeneracy.s_comp_π_…CategoryTheory.Limits.WidePullback.hom_ext · cited by 1WidePullback.hom_extCategoryTheory.Limits.WidePullback.lift_base_assoc · cited by 0WidePullback.lift_base_as…CategoryTheory.Limits.WidePullback.π_arrow_assoc · cited by 0WidePullback.π_arrow_assocCategoryTheory.Arrow.augmentedCechNerve_hom_app · cited by 0Arrow.augmentedCechNerve_…CategoryTheory.SimplicialObject.augmentedCechNerve_map_left_app · cited by 0SimplicialObject.augmente…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.limit.π · cited by 278limit.πCategoryTheory.Limits.HasWidePullback · cited by 44Limits.HasWidePullbackCategoryTheory.Limits.widePullback · cited by 31Limits.widePullbackCategoryTheory.Limits.WidePullbackShape.wideCospan · cited by 22WidePullbackShape.wideCos…WidePullback.baseCITED BYCITES

Cites6

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

Cited by24

Results whose statement or proof uses this declaration.