Theorems · Theorem · category theory
TopCat.Sheaf.IsFlasque.structured_arrows_elements_sheaf_chains_bounded
∀ {X : TopCat} {U : TopologicalSpace.Opens ↑X} {F G : TopCat.Sheaf AddCommGrpCat X} (g : F ⟶ G)
(s : ↑(G.obj.obj (Opposite.op U))) (c : Set (TopCat.Sheaf.IsFlasque.Under g s)),
IsChain (fun x y => Nonempty (y ⟶ x)) c → ∃ ub, ∀ a ∈ c, Nonempty (ub ⟶ a)- Defined in
- Mathlib.Topology.Sheaves.Flasque
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites53
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositestatement · cited by 8,081
- Set.Elemproof · cited by 7,166
- CategoryTheory.Functor.compstatement and proof · cited by 6,529
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- AddMonoidHomstatement · cited by 3,230
Cited by1
Results whose statement or proof uses this declaration.
- TopCat.Sheaf.IsFlasque.epi_of_shortExactproof · cited by 1