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Theorems · Definition · category theory

CategoryTheory.MonoOver.forget

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    (X : C) → CategoryTheory.Functor (CategoryTheory.MonoOver X) (CategoryTheory.Over X)

The inclusion from monomorphisms over X to morphisms over X.

Defined in
Mathlib.CategoryTheory.Subobject.MonoOver
Cited by
23 results in Mathlib
Foundations
Depth 29 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.

CategoryTheory.Subobject.underlying · cited by 211Subobject.underlyingCategoryTheory.Subobject.underlyingIso · cited by 41Subobject.underlyingIsoCategoryTheory.Subobject.underlyingIso_arrow · cited by 22Subobject.underlyingIso_a…CategoryTheory.MonoOver.lift · cited by 8MonoOver.liftCategoryTheory.SubobjectRepresentableBy.iso_inv_left_π · cited by 3SubobjectRepresentableBy.…CategoryTheory.MonoOver.image · cited by 3MonoOver.imageCategoryTheory.IsGrothendieckAbelian.exists_isIso_of_functor_from_monoOver · cited by 2IsGrothendieckAbelian.exi…CategoryTheory.IsGrothendieckAbelian.mono_of_isColimit_monoOver · cited by 2IsGrothendieckAbelian.mon…CategoryTheory.MonoOver.inf · cited by 2MonoOver.infCategoryTheory.SubobjectRepresentableBy.isPullback · cited by 1SubobjectRepresentableBy.…CategoryTheory.Subobject.Classifier.χ_pullback_obj_mk_truth_arrow · cited by 1Classifier.χ_pullback_obj…CategoryTheory.MonoOver.exists · cited by 1MonoOver.existsCategoryTheory.MonoOver.existsIsoMap · cited by 1MonoOver.existsIsoMapCategoryTheory.MonoOver.factors_congr · cited by 1MonoOver.factors_congrCategoryTheory.Subobject.map_pullback · cited by 1Subobject.map_pullbackCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Over · cited by 935CategoryTheory.OverCategoryTheory.MonoOver · cited by 115CategoryTheory.MonoOverCategoryTheory.Over.isMono · cited by 111Over.isMonoCategoryTheory.ObjectProperty.ι · cited by 95ObjectProperty.ιMonoOver.forgetCITED BYCITES

Cites6

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

Cited by47

Results whose statement or proof uses this declaration.