Theorems · Definition · category theory
CategoryTheory.Subobject
{C : Type u₁} → [CategoryTheory.Category.{v₁, u₁} C] → C → Type (max u₁ v₁)The category of subobjects of X : C, defined as isomorphism classes of monomorphisms into X.
- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 385 results in Mathlib
- Foundations
- Depth 29 from the axioms, rests on 166 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.MonoOverproof · cited by 115
- CategoryTheory.ThinSkeletonproof · cited by 17
Cited by501
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.underlyingstatement · cited by 211
- CategoryTheory.Subobject.arrowstatement and proof · cited by 175
- CategoryTheory.Subobject.mkstatement · cited by 109
- CategoryTheory.Limits.kernelSubobjectstatement · cited by 58
- CategoryTheory.Subobject.Factorsstatement and proof · cited by 56
- CategoryTheory.Subobject.pullbackstatement · cited by 54
- CategoryTheory.Limits.imageSubobjectstatement · cited by 53
- CategoryTheory.Subobject.underlyingIsostatement · cited by 41
- CategoryTheory.Subobject.ofLEstatement and proof · cited by 38
- CategoryTheory.Subobject.factorThrustatement and proof · cited by 35
- CategoryTheory.Subobject.eq_of_comp_arrow_eqstatement and proof · cited by 31
- CategoryTheory.Subobject.factorThru_arrowstatement and proof · cited by 31
Showing the 200 most cited of 501.