Theorems · Definition · category theory
CategoryTheory.Subobject.representative
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{X : C} → CategoryTheory.Functor (CategoryTheory.Subobject X) (CategoryTheory.MonoOver X)Use choice to pick a representative MonoOver X for each Subobject X.
- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 35 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.
Cites8
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.Equivalence.functorproof · cited by 1,268
- CategoryTheory.Overstatement · cited by 935
- CategoryTheory.Subobjectstatement · cited by 385
- CategoryTheory.MonoOverstatement · cited by 115
- CategoryTheory.Over.isMonostatement · cited by 111
- CategoryTheory.Subobject.equivMonoOverproof · cited by 4
Cited by22
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.underlyingproof · cited by 211
- CategoryTheory.Subobject.arrowproof · cited by 175
- CategoryTheory.Subobject.factors_iffstatement · cited by 12
- CategoryTheory.SubobjectRepresentableBy.isostatement and proof · cited by 7
- CategoryTheory.Subobject.factors_of_leproof · cited by 5
- CategoryTheory.SubobjectRepresentableBy.iso_inv_hom_left_compstatement · cited by 3
- CategoryTheory.SubobjectRepresentableBy.iso_inv_left_πstatement and proof · cited by 3
- CategoryTheory.Subobject.underlying_arrowproof · cited by 3
- CategoryTheory.Subobject.representativeIsostatement · cited by 2
- CategoryTheory.isNoetherianObject_iff_isEventuallyConstantproof · cited by 1
- CategoryTheory.isArtinianObject_iff_isEventuallyConstantproof · cited by 1
- CategoryTheory.Subobject.thinSkeleton_mk_representative_eq_selfstatement and proof · cited by 1