Theorems · Theorem · category theory
CategoryTheory.Subobject.ofLE_comp_ofLE
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {B : C} (X Y Z : CategoryTheory.Subobject B) (h₁ : X ≤ Y)
(h₂ : Y ≤ Z), CategoryTheory.CategoryStruct.comp (X.ofLE Y h₁) (Y.ofLE Z h₂) = X.ofLE Z ⋯- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 38 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.
Cites12
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Functorproof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- LE.le.transstatement and proof · cited by 3,151
- CategoryTheory.Functor.map_compproof · cited by 734
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.Subobject.underlyingstatement and proof · cited by 211
- CategoryTheory.Subobject.ofLEstatement · cited by 38
- LE.le.homproof · cited by 30
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.ofLE_comp_ofLE_assocproof · cited by 0