Theorems · Definition · category theory
CategoryTheory.MorphismProperty.monomorphisms
(C : Type u) → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty CThe MorphismProperty C satisfied by monomorphisms in C.
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.MorphismPropertystatement · cited by 2,179
- CategoryTheory.Monoproof · cited by 893
Cited by41
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.monomorphisms.infer_propertystatement · cited by 6
- CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms_le_monomorphismsstatement · cited by 2
- SSet.rlp_monomorphismsstatement and proof · cited by 2
- AlgebraicGeometry.IsClosedImmersion.iff_isFinite_and_monoproof · cited by 2
- CategoryTheory.MorphismProperty.presheaf_mono_of_lestatement and proof · cited by 2
- CategoryTheory.Limits.colim.map_mono'proof · cited by 2
- CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms_rlpstatement and proof · cited by 1
- CategoryTheory.IsGrothendieckAbelian.monoMapFactorizationDataRlpstatement and proof · cited by 1
- CategoryTheory.ConcreteCategory.injective_eq_monomorphisms_iffstatement and proof · cited by 1
- CategoryTheory.ConcreteCategory.injective_le_monomorphismsstatement · cited by 1
- CategoryTheory.ShortComplex.exact_iff_mono_cokernel_descproof · cited by 1
- CategoryTheory.ObjectProperty.SerreClassLocalization.mono_iffproof · cited by 1