Theorems · Theorem · category theory
CategoryTheory.Subobject.ofLE_comp_ofLE_assoc
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {B : C} (X Y Z : CategoryTheory.Subobject B) (h₁ : X ≤ Y)
(h₂ : Y ≤ Z) {Z_1 : C} (h : CategoryTheory.Subobject.underlying.obj Z ⟶ Z_1),
CategoryTheory.CategoryStruct.comp (X.ofLE Y h₁) (CategoryTheory.CategoryStruct.comp (Y.ofLE Z h₂) h) =
CategoryTheory.CategoryStruct.comp (X.ofLE Z ⋯) h- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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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.Functor.objstatement and proof · 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.Subobjectstatement and proof · cited by 385
- CategoryTheory.Subobject.underlyingstatement and proof · cited by 211
- CategoryTheory.Subobject.ofLEstatement and proof · cited by 38
- CategoryTheory.Subobject.ofLE_comp_ofLEproof · cited by 2
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