Theorems · Theorem · category theory

CategoryTheory.Limits.image.factorThruImage_preComp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y) {Z : C} (g : Y ⟶ Z)
  [inst_1 : CategoryTheory.Limits.HasImage g]
  [inst_2 : CategoryTheory.Limits.HasImage (CategoryTheory.CategoryStruct.comp f g)],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.factorThruImage (CategoryTheory.CategoryStruct.comp f g))
      (CategoryTheory.Limits.image.preComp f g) =
    CategoryTheory.CategoryStruct.comp f (CategoryTheory.Limits.factorThruImage g)

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Images
Cited by: 1 results in Mathlib
Foundations: Depth 11 from the axioms · uses propext, Classical.choice
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasImage CategoryTheory.Limits.HasImage

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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.Limits.imagestatement and proof · cited by 124
CategoryTheory.Limits.HasImagestatement and proof · cited by 107
CategoryTheory.Limits.image.ιproof · cited by 104
CategoryTheory.Limits.factorThruImagestatement and proof · cited by 55
CategoryTheory.Limits.image.preCompstatement · cited by 7
CategoryTheory.Limits.image.fac_liftproof · cited by 5

Cited by1

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CategoryTheory.Limits.image.factorThruImage_preComp_assocproof · cited by 0