Theorems · Theorem · category theory
TopCat.Sheaf.IsFlasque.epi_of_shortExact
∀ {X : TopCat} {U : TopologicalSpace.Opens ↑X} {S : CategoryTheory.ShortComplex (TopCat.Sheaf AddCommGrpCat X)},
S.ShortExact → ∀ [S.X₁.IsFlasque], CategoryTheory.Epi (S.g.hom.app (Opposite.op U))Given a short exact sequence of sheaves, 0 ⟶ 𝓕 ⟶ 𝓖 ⟶ 𝓗 ⟶ 0, if 𝓕 is flasque then
𝓖(U) ⟶ 𝓗(U) is surjective, for any open U.
- Defined in
- Mathlib.Topology.Sheaves.Flasque
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopCat.Sheaf.IsFlasque
Around this declaration
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Cites96
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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Cited by1
Results whose statement or proof uses this declaration.
- TopCat.Sheaf.IsFlasque.of_shortExact_of_isFlasque₁₂proof · cited by 0