Theorems · Theorem · category theory

TopCat.partialSections.closed

∀ {J : Type u} [inst : CategoryTheory.SmallCategory J] (F : CategoryTheory.Functor J TopCat)
  [∀ (j : J), T2Space ↑(F.obj j)] {G : Finset J} (H : Finset (TopCat.FiniteDiagramArrow✝ G)),
  IsClosed (TopCat.partialSections F H)

Defined in: Mathlib.Topology.Category.TopCat.Limits.Konig
Cited by: 1 results in Mathlib
Foundations: Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.SmallCategory T2Space

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Cites23

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

DFunLike.coeproof · cited by 62,936
Setproof · cited by 53,352
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
Finsetstatement and proof · cited by 13,712
CategoryTheory.Functor.mapproof · cited by 8,698
SetLike.coeproof · cited by 8,199
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CategoryTheory.ConcreteCategory.homproof · cited by 4,022
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TopCatstatement and proof · cited by 1,889

Cited by1

Results whose statement or proof uses this declaration.

TopCat.nonempty_limitCone_of_compact_t2_cofiltered_systemproof · cited by 2