Theorems · Definition · category theory

TopCat.LocalPredicate.cocone

{X : TopCat} →
  {T : ↑X → Type u_1} →
    (P : TopCat.LocalPredicate T) →
      (x : ↑X) →
        CategoryTheory.Limits.Cocone
          ((TopologicalSpace.OpenNhds.inclusion x).op.comp (TopCat.subpresheafToTypes P.toPrelocalPredicate))

Auxiliary definition for stalkToFiber.

Defined in: Mathlib.Topology.Sheaves.LocalPredicate
Cited by: 3 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

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

Cites14

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

CategoryTheory.Functor.objproof · cited by 19,642
Oppositestatement and proof · cited by 8,081
CategoryTheory.Functor.compstatement and proof · cited by 6,529
TopCat.carrierstatement and proof · cited by 3,184
TopologicalSpace.Opensstatement · cited by 2,040
TopCatstatement and proof · cited by 1,889
CategoryTheory.Functor.opstatement and proof · cited by 997
CategoryTheory.Limits.Coconestatement · cited by 746
TypeCat.ofHomproof · cited by 389
TopologicalSpace.OpenNhdsstatement and proof · cited by 61
TopCat.LocalPredicate.toPrelocalPredicatestatement and proof · cited by 48
TopologicalSpace.OpenNhds.inclusionstatement and proof · cited by 44

Cited by4

Results whose statement or proof uses this declaration.

TopCat.stalkToFiberproof · cited by 4
smoothSheaf.ι_evalHomproof · cited by 3
TopCat.stalkToFiber_germproof · cited by 2
TopCat.stalkToFiber_ιstatement and proof · cited by 1