Theorems · Theorem · category theory
CategoryTheory.Subobject.ofMkLEMk_comp_ofMkLEMk_assoc
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {B A₁ A₂ A₃ : C} (f : A₁ ⟶ B)
[inst_1 : CategoryTheory.Mono f] (g : A₂ ⟶ B) [inst_2 : CategoryTheory.Mono g] (h : A₃ ⟶ B)
[inst_3 : CategoryTheory.Mono h] (h₁ : CategoryTheory.Subobject.mk f ≤ CategoryTheory.Subobject.mk g)
(h₂ : CategoryTheory.Subobject.mk g ≤ CategoryTheory.Subobject.mk h) {Z : C} (h_1 : A₃ ⟶ Z),
CategoryTheory.CategoryStruct.comp (CategoryTheory.Subobject.ofMkLEMk f g h₁)
(CategoryTheory.CategoryStruct.comp (CategoryTheory.Subobject.ofMkLEMk g h h₂) h_1) =
CategoryTheory.CategoryStruct.comp (CategoryTheory.Subobject.ofMkLEMk f h ⋯) h_1- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- LE.le.transstatement and proof · cited by 3,151
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Subobjectstatement · cited by 385
- CategoryTheory.Subobject.mkstatement and proof · cited by 109
- CategoryTheory.Subobject.ofMkLEMkstatement and proof · cited by 18
- CategoryTheory.Subobject.ofMkLEMk_comp_ofMkLEMkproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.