Theorems · Theorem · category theory
CategoryTheory.Subobject.ofLEMk_comp_ofMkLE_assoc
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {B A : C} (X : CategoryTheory.Subobject B) (f : A ⟶ B)
[inst_1 : CategoryTheory.Mono f] (Y : CategoryTheory.Subobject B) (h₁ : X ≤ CategoryTheory.Subobject.mk f)
(h₂ : CategoryTheory.Subobject.mk f ≤ Y) {Z : C} (h : CategoryTheory.Subobject.underlying.obj Y ⟶ Z),
CategoryTheory.CategoryStruct.comp (X.ofLEMk f h₁)
(CategoryTheory.CategoryStruct.comp (CategoryTheory.Subobject.ofMkLE f Y h₂) h) =
CategoryTheory.CategoryStruct.comp (X.ofLE Y ⋯) 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 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.Monostatement and proof · cited by 893
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.Subobject.underlyingstatement and proof · cited by 211
- CategoryTheory.Subobject.mkstatement and proof · cited by 109
- CategoryTheory.Subobject.ofLEstatement and proof · cited by 38
- CategoryTheory.Subobject.ofLEMkstatement and proof · cited by 13
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