Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.presheaf_mono_of_le
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P : CategoryTheory.MorphismProperty C}
{G : CategoryTheory.Functor Cᵒᵖ (Type v₁)},
P ≤ CategoryTheory.MorphismProperty.monomorphisms C →
∀ {X : C} {f : CategoryTheory.yoneda.obj X ⟶ G}, P.presheaf f → CategoryTheory.Mono f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 63 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.
Cites12
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.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Monostatement · cited by 893
- CategoryTheory.yonedastatement and proof · cited by 351
- CategoryTheory.MorphismProperty.monomorphismsstatement and proof · cited by 39
- CategoryTheory.MorphismProperty.presheafstatement and proof · cited by 17
- CategoryTheory.MorphismProperty.relative_monotoneproof · cited by 1
- CategoryTheory.MorphismProperty.presheaf_monomorphisms_le_monomorphismsproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.fst'_self_eq_sndproof · cited by 0
- CategoryTheory.MorphismProperty.isIso_fst'_selfproof · cited by 0