Theorems · Theorem · general topology

TopCat.GlueData.preimage_image_eq_image

∀ (D : TopCat.GlueData) (i j : D.J) (U : Set ↑(D.U i)),
  ⇑(CategoryTheory.ConcreteCategory.hom (D.ι j)) ⁻¹' ⇑(CategoryTheory.ConcreteCategory.hom (D.ι i)) '' U =
    ⇑(CategoryTheory.ConcreteCategory.hom (D.f j i)) ''
      ⇑(CategoryTheory.ConcreteCategory.hom (CategoryTheory.CategoryStruct.comp (D.t j i) (D.f i j))) ⁻¹' U

Defined in: Mathlib.Topology.Gluing
Cited by: 2 results in Mathlib
Foundations: Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites35

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

DFunLike.coestatement and proof · cited by 62,936
Setstatement and proof · cited by 53,352
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
Set.imagestatement and proof · cited by 5,609
Set.preimagestatement and proof · cited by 4,946
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
TopCat.carrierstatement and proof · cited by 3,184
ContinuousMapstatement · cited by 2,491
Set.extproof · cited by 2,266
TopCatstatement · cited by 1,889
Set.image_congrproof · cited by 533
TopCat.Hom.homproof · cited by 169

Cited by2

Results whose statement or proof uses this declaration.

TopCat.GlueData.open_image_openproof · cited by 1
TopCat.GlueData.preimage_image_eq_image'proof · cited by 1