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Theorems · Definition · category theory

CategoryTheory.MonoOver.mk

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X A : C} → (f : A ⟶ X) → [hf : CategoryTheory.Mono f] → CategoryTheory.MonoOver X

Construct a MonoOver X.

Defined in
Mathlib.CategoryTheory.Subobject.MonoOver
Cited by
33 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Mono

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Subobject.mk · cited by 109Subobject.mkCategoryTheory.Subobject.underlyingIso · cited by 41Subobject.underlyingIsoCategoryTheory.Subobject.underlyingIso_arrow · cited by 22Subobject.underlyingIso_a…CategoryTheory.Abelian.Preradical.colon · cited by 13Preradical.colonCategoryTheory.Subfunctor.equivalenceMonoOver · cited by 8Subfunctor.equivalenceMon…CategoryTheory.SubobjectRepresentableBy.iso · cited by 7SubobjectRepresentableBy.…Types.monoOverEquivalenceSet · cited by 6Types.monoOverEquivalence…CategoryTheory.Subobject.mk_arrow · cited by 4Subobject.mk_arrowCategoryTheory.SubobjectRepresentableBy.iso_inv_hom_left_comp · cited by 3SubobjectRepresentableBy.…CategoryTheory.SubobjectRepresentableBy.iso_inv_left_π · cited by 3SubobjectRepresentableBy.…CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.F · cited by 3injectivity₀.FCategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.F · cited by 3surjectivity.FCategoryTheory.MonoOver.imageMonoOver · cited by 3MonoOver.imageMonoOverCategoryTheory.Subobject.pullback_obj_mk · cited by 3Subobject.pullback_obj_mkCategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver · cited by 2generatingMonomorphisms.f…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Mono · cited by 893CategoryTheory.MonoCategoryTheory.Over.mk · cited by 203Over.mkCategoryTheory.MonoOver · cited by 115CategoryTheory.MonoOverMonoOver.mkCITED BYCITES

Cites5

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

Cited by49

Results whose statement or proof uses this declaration.