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Theorems · Definition · category theory

CategoryTheory.MorphismProperty.monomorphisms

(C : Type u) → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C

The MorphismProperty C satisfied by monomorphisms in C.

Defined in
Mathlib.CategoryTheory.MorphismProperty.Basic
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.

CategoryTheory.MorphismProperty.monomorphisms.infer_property · cited by 6monomorphisms.infer_prope…CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms_le_monomorphisms · cited by 2IsGrothendieckAbelian.gen…SSet.rlp_monomorphisms · cited by 2SSet.rlp_monomorphismsAlgebraicGeometry.IsClosedImmersion.iff_isFinite_and_mono · cited by 2IsClosedImmersion.iff_isF…CategoryTheory.MorphismProperty.presheaf_mono_of_le · cited by 2MorphismProperty.presheaf…CategoryTheory.Limits.colim.map_mono' · cited by 2colim.map_mono'CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms_rlp · cited by 1IsGrothendieckAbelian.gen…CategoryTheory.IsGrothendieckAbelian.monoMapFactorizationDataRlp · cited by 1IsGrothendieckAbelian.mon…CategoryTheory.ConcreteCategory.injective_eq_monomorphisms_iff · cited by 1ConcreteCategory.injectiv…CategoryTheory.ConcreteCategory.injective_le_monomorphisms · cited by 1ConcreteCategory.injectiv…CategoryTheory.ShortComplex.exact_iff_mono_cokernel_desc · cited by 1ShortComplex.exact_iff_mo…CategoryTheory.ObjectProperty.SerreClassLocalization.mono_iff · cited by 1SerreClassLocalization.mo…CategoryTheory.MorphismProperty.presheaf_monomorphisms_le_monomorphisms · cited by 1MorphismProperty.presheaf…CategoryTheory.Preadditive.mono_iff_injective' · cited by 1Preadditive.mono_iff_inje…SSet.modelCategoryQuillen.I_le_monomorphisms · cited by 1modelCategoryQuillen.I_le…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.Mono · cited by 893CategoryTheory.MonoMorphismProperty.monomorphismsCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by41

Results whose statement or proof uses this declaration.