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.
- 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.
Cites6
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
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Overstatement · cited by 935
- CategoryTheory.MonoOverstatement · cited by 115
- CategoryTheory.Over.isMonostatement and proof · cited by 111
- CategoryTheory.ObjectProperty.ιproof · cited by 95
Cited by47
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.underlyingproof · cited by 211
- CategoryTheory.Subobject.underlyingIsoproof · cited by 41
- CategoryTheory.Subobject.underlyingIso_arrowproof · cited by 22
- CategoryTheory.MonoOver.liftstatement and proof · cited by 8
- CategoryTheory.SubobjectRepresentableBy.iso_inv_left_πproof · cited by 3
- CategoryTheory.MonoOver.imageproof · cited by 3
- CategoryTheory.IsGrothendieckAbelian.exists_isIso_of_functor_from_monoOverstatement and proof · cited by 2
- CategoryTheory.IsGrothendieckAbelian.mono_of_isColimit_monoOverstatement and proof · cited by 2
- CategoryTheory.MonoOver.infproof · cited by 2
- CategoryTheory.SubobjectRepresentableBy.isPullbackproof · cited by 1
- CategoryTheory.Subobject.Classifier.χ_pullback_obj_mk_truth_arrowproof · cited by 1
- CategoryTheory.MonoOver.existsproof · cited by 1