Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.isLocal_iSup
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {ι : Sort u_1} (W : ι → CategoryTheory.MorphismProperty C),
(⨆ i, W i).isLocal = ⨅ i, (W i).isLocal- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 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.
Cites11
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.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- iSupstatement and proof · cited by 2,415
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- iInfstatement and proof · cited by 1,690
- Function.Bijectiveproof · cited by 863
- CategoryTheory.ObjectPropertystatement · cited by 798
- CategoryTheory.MorphismProperty.isLocalstatement · cited by 22
- iInf_applyproof · cited by 15
- iInf_Prop_eqproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Presheaf.preservesLimitsOfShape_eq_isLocalproof · cited by 0