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Theorems · Theorem · category theory

TopCat.pullback_topology

∀ {X Y Z : TopCat} (f : X ⟶ Z) (g : Y ⟶ Z),
  (CategoryTheory.Limits.pullback f g).str =
    TopologicalSpace.induced (⇑(CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.pullback.fst f g))) X.str ⊓
      TopologicalSpace.induced (⇑(CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.pullback.snd f g))) Y.str
Defined in
Mathlib.Topology.Category.TopCat.Limits.Pullbacks
Cited by
1 results in Mathlib
Foundations
Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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TopCat.isInducing_pullback_to_prod · cited by 1TopCat.isInducing_pullbac…DFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomTopologicalSpace · cited by 24529TopologicalSpaceCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.carrier · cited by 3184TopCat.carrierContinuousMap · cited by 2491ContinuousMapTopCat · cited by 1889TopCatCategoryTheory.Limits.WalkingPair · cited by 1319Limits.WalkingPairCategoryTheory.Limits.pullback · cited by 864Limits.pullbackHomeomorph · cited by 725HomeomorphCategoryTheory.Limits.pullback.fst · cited by 639pullback.fstCategoryTheory.Limits.pullback.snd · cited by 637pullback.sndCategoryTheory.Limits.WalkingCospan · cited by 496Limits.WalkingCospanCategoryTheory.Limits.cospan · cited by 467Limits.cospanTopologicalSpace.induced · cited by 148TopologicalSpace.inducedTopCat.pullback_topologyCITED BYCITES

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