Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.presheaf_monomorphisms_le_monomorphisms

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C],
  (CategoryTheory.MorphismProperty.monomorphisms C).presheaf ≤
    CategoryTheory.MorphismProperty.monomorphisms (CategoryTheory.Functor Cᵒᵖ (Type v₁))

Morphisms satisfying (monomorphism C).presheaf are in particular monomorphisms.

Defined in: Mathlib.CategoryTheory.MorphismProperty.Representable
Cited by: 1 results in Mathlib
Foundations: Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites27

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.Functor.objproof · cited by 19,642
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Functorstatement and proof · cited by 16,252
Oppositestatement and proof · cited by 8,081
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.MorphismPropertystatement · cited by 2,179
CategoryTheory.Category.id_compproof · cited by 1,998
CategoryTheory.Monoproof · cited by 893
CategoryTheory.Functor.map_idproof · cited by 616

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.MorphismProperty.presheaf_mono_of_leproof · cited by 2