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Theorems · Theorem · category theory

TopCat.pullback_snd_image_fst_preimage

∀ {X Y Z : TopCat} (f : X ⟶ Z) (g : Y ⟶ Z) (U : Set ↑X),
  ⇑(CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.pullback.snd f g)) ''
      ⇑(CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.pullback.fst f g)) ⁻¹' U =
    ⇑(CategoryTheory.ConcreteCategory.hom g) ⁻¹' ⇑(CategoryTheory.ConcreteCategory.hom f) '' U
Defined in
Mathlib.Topology.Category.TopCat.Limits.Pullbacks
Cited by
2 results in Mathlib
Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

AlgebraicGeometry.IsOpenImmersion.range_pullbackSnd · cited by 4IsOpenImmersion.range_pul…AlgebraicGeometry.PresheafedSpace.GlueData.pullback_base · cited by 0GlueData.pullback_baseDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Iso.inv · cited by 6514Iso.invSet.image · cited by 5609Set.imageSet.preimage · cited by 4946Set.preimageCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.carrier · cited by 3184TopCat.carrierContinuousMap · cited by 2491ContinuousMapSet.ext · cited by 2266Set.extTopCat · cited by 1889TopCatCategoryTheory.Limits.WalkingPair · cited by 1319Limits.WalkingPairCategoryTheory.Limits.pullback · cited by 864Limits.pullbackCategoryTheory.Limits.pullback.fst · cited by 639pullback.fstCategoryTheory.Limits.pullback.snd · cited by 637pullback.sndTopCat.pullback_snd_image_fst…CITED BYCITES

Cites22

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Cited by2

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