Theorems · Theorem · category theory
TopCat.Presheaf.presheafEquivOfIso_unitIso_hom_app_app
∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] {X Y : TopCat} (H : X ≅ Y)
(X_1 : CategoryTheory.Functor (TopologicalSpace.Opens ↑X)ᵒᵖ C) (X_2 : (TopologicalSpace.Opens ↑X)ᵒᵖ),
((TopCat.Presheaf.presheafEquivOfIso C H).unitIso.hom.app X_1).app X_2 = X_1.map (CategoryTheory.eqToHom ⋯)- Defined in
- Mathlib.Topology.Sheaves.Presheaf
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.NatTrans.appstatement · cited by 7,406
- CategoryTheory.Functor.compstatement · cited by 6,529
- CategoryTheory.Iso.invstatement and proof · cited by 6,514
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
Cited by1
Results whose statement or proof uses this declaration.
- TopCat.Presheaf.toPushforwardOfIso_appproof · cited by 0