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abbrev IsQuasicoherent_Def24 {C : Type u_1} [CategoryTheory.Category.{u_2, u_1} C] {J : CategoryTheory.GrothendieckTopology C} {R : CategoryTheory.Sheaf J RingCat} [∀ (X : C), (J.over X).HasSheafCompose (CategoryTheory.forget₂ RingCat AddCommGrpCat)] [∀ (X : C), CategoryTheory.HasWeakSheafify (J.over X) AddCommGrpCat] [∀ (X : C), (J.over X).WEqualsLocallyBijective AddCommGrpCat] (F : SheafOfModules R) : Prop

Definition 24 (Lec 10): a sheaf of O_X-modules F is quasi-coherent if it is locally a cokernel of a map between free sheaves; abbreviates SheafOfModules.IsQuasicoherent.