Theorems · Theorem · category theory
CategoryTheory.Subobject.ofMkLE_comp_ofLE
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {B A₁ : C} (f : A₁ ⟶ B) [inst_1 : CategoryTheory.Mono f]
(X Y : CategoryTheory.Subobject B) (h₁ : CategoryTheory.Subobject.mk f ≤ X) (h₂ : X ≤ Y),
CategoryTheory.CategoryStruct.comp (CategoryTheory.Subobject.ofMkLE f X h₁) (X.ofLE Y h₂) =
CategoryTheory.Subobject.ofMkLE f Y ⋯- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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 and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- LE.le.transstatement and proof · cited by 3,151
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Functor.map_compproof · cited by 734
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.CategoryStructproof · cited by 343
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.ofMkLE_comp_ofLE_assocproof · cited by 0