Theorems · Theorem · category theory
CategoryTheory.Presieve.pushforward_ofArrows
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {ι : Type u_1} {U : ι → C} {X Y : C} (g : (i : ι) → U i ⟶ X)
(f : X ⟶ Y),
CategoryTheory.Presieve.pushforward f (CategoryTheory.Presieve.ofArrows U g) =
CategoryTheory.Presieve.ofArrows U fun x => CategoryTheory.CategoryStruct.comp (g x) f- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 26 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.
Cites9
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 and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- le_antisymmproof · cited by 2,068
- CategoryTheory.Presievestatement · cited by 449
- CategoryTheory.Presieve.ofArrowsstatement and proof · cited by 150
- CategoryTheory.Presieve.ofArrows.casesOnproof · cited by 64
- CategoryTheory.Presieve.pushforwardstatement and proof · cited by 13
- CategoryTheory.Presieve.ofArrows_le_iffproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Presieve.pushforward_singletonproof · cited by 0
- CategoryTheory.PreZeroHypercover.presieve₀_pushforwardproof · cited by 0