Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.sInf_iff
∀ {C : Type u} [inst : CategoryTheory.CategoryStruct.{v, u} C] (S : Set (CategoryTheory.MorphismProperty C)) {X Y : C}
(f : X ⟶ Y), sInf S f ↔ ∀ W ∈ S, W f- Cited by
- 4 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- InfSet.sInfstatement · cited by 935
- CategoryTheory.CategoryStructstatement and proof · cited by 343
- iInf_applyproof · cited by 15
- iInf_Prop_eqproof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.RespectsRight.sInfproof · cited by 1
- CategoryTheory.MorphismProperty.RespectsLeft.sInfproof · cited by 1
- CategoryTheory.MorphismProperty.IsStableUnderComposition.sInfproof · cited by 1
- CategoryTheory.MorphismProperty.ContainsIdentities.sInfproof · cited by 1