Theorems · Theorem · category theory

CategoryTheory.Injective.comp_factorThru_assoc

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J X Y : C} [inst_1 : CategoryTheory.Injective J]
  (g : X ⟶ J) (f : X ⟶ Y) [inst_2 : CategoryTheory.Mono f] {Z : C} (h : J ⟶ Z),
  CategoryTheory.CategoryStruct.comp f
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Injective.factorThru g f) h) =
    CategoryTheory.CategoryStruct.comp g h

Defined in: Mathlib.CategoryTheory.Preadditive.Injective.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 11 from the axioms · uses Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Injective CategoryTheory.Mono

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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
CategoryTheory.Monostatement and proof · cited by 893
CategoryTheory.Injectivestatement and proof · cited by 70
CategoryTheory.Injective.factorThrustatement and proof · cited by 12
CategoryTheory.Injective.comp_factorThruproof · cited by 10

Cited by1

Results whose statement or proof uses this declaration.

CochainComplex.isSplitMono_from_singleFunctor_obj_of_injectiveproof · cited by 1