Theorems · Theorem · category theory
CategoryTheory.Subobject.ofMkLE_comp_ofLEMk_assoc
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {B A₁ A₂ : C} (f : A₁ ⟶ B) [inst_1 : CategoryTheory.Mono f]
(X : CategoryTheory.Subobject B) (g : A₂ ⟶ B) [inst_2 : CategoryTheory.Mono g]
(h₁ : CategoryTheory.Subobject.mk f ≤ X) (h₂ : X ≤ CategoryTheory.Subobject.mk g) {Z : C} (h : A₂ ⟶ Z),
CategoryTheory.CategoryStruct.comp (CategoryTheory.Subobject.ofMkLE f X h₁)
(CategoryTheory.CategoryStruct.comp (X.ofLEMk g h₂) h) =
CategoryTheory.CategoryStruct.comp (CategoryTheory.Subobject.ofMkLEMk f g ⋯) h- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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.Category.assocproof · cited by 6,433
- LE.le.transstatement and proof · cited by 3,151
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.Subobject.underlyingstatement · cited by 211
- CategoryTheory.Subobject.mkstatement and proof · cited by 109
- CategoryTheory.Subobject.ofMkLEMkstatement and proof · cited by 18
- CategoryTheory.Subobject.ofLEMkstatement and proof · cited by 13
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