Theorems · Definition · category theory

TopCat.Presheaf.Pushforward.id

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X : TopCat} →
      (ℱ : TopCat.Presheaf C X) → (TopCat.Presheaf.pushforward C (CategoryTheory.CategoryStruct.id X)).obj ℱ ≅ ℱ

The natural isomorphism between the pushforward of a presheaf along the identity continuous map and the original presheaf.

Defined in: Mathlib.Topology.Sheaves.Presheaf
Cited by: 5 results in Mathlib
Foundations: Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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

Cites8

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

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
CategoryTheory.Isostatement · cited by 3,963
TopCatstatement and proof · cited by 1,889
CategoryTheory.Iso.reflproof · cited by 727
TopCat.Presheafstatement and proof · cited by 371
TopCat.Presheaf.pushforwardstatement and proof · cited by 174

Cited by5

Results whose statement or proof uses this declaration.

AlgebraicGeometry.PresheafedSpace.stalkMap.idproof · cited by 2
TopCat.Presheaf.stalkPushforward.idstatement and proof · cited by 1
AlgebraicGeometry.PresheafedSpace.map_id_c_appstatement · cited by 0
TopCat.Presheaf.Pushforward.id_hom_appstatement · cited by 0
TopCat.Presheaf.Pushforward.id_inv_appstatement · cited by 0